Quick Answer
SAT triangle practice questions test angle sums, exterior angles, side-length relationships, area, perimeter, isosceles and equilateral properties, right triangles, special triangles, similarity, congruence, and scale factors. This guide includes 70 SAT-style questions that progress from basic triangle facts to Pythagorean theorem problems, 30-60-90 and 45-45-90 triangles, area scaling, and harder mixed geometry models.
What Should You Know Before Practicing Triangles?
- The interior angles of a triangle sum to 180°.
- An exterior angle equals the sum of the two remote interior angles.
- The sum of any two side lengths must be greater than the third side.
- Larger angles are opposite longer sides.
- Right triangles satisfy a²+b²=c².
- A 45-45-90 triangle has side ratio 1:1:√2.
- A 30-60-90 triangle has side ratio 1:√3:2.
- Similar figures scale in length by k and in area by k².
In This Guide – 70 SAT Triangles Practice Questions
Start With SAT Math Topic-Wise Practice
Connect triangle practice with weekly score planning, mock-test review, and targeted SAT Math correction.
Download the SAT Prep Guide E-Book
Use the SAT Prep Guide E-Book to organize triangle geometry, right-triangle, similarity, and data-analysis practice with a clear weekly score improvement plan.
Download SAT Prep E-Book Guide Download SAT Prep Guide E-BookWhat Does the SAT Test in Triangle Questions?
Students may need to use angle relationships, calculate area or perimeter, apply the Pythagorean theorem, identify a special triangle, compare corresponding sides, or solve a similarity and scale-factor model.
| Skill Area | What It Tests | Questions |
|---|---|---|
| Triangle basics | Angle sums, side classification, perimeter, and area | Q1-Q15 |
| Angle relationships | Isosceles, equilateral, exterior angles, and side-angle order | Q16-Q30 |
| Right triangles | Pythagorean theorem and special-triangle ratios | Q31-Q45 |
| Similarity and advanced models | Scale factors, area ratios, congruence, and mixed geometry | Q46-Q70 |
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How Are Triangle Basics Tested?
These questions focus on angle sums, side-length rules, triangle classification, perimeter, and area.
TRIANGLE BASICS
EASY
Question 1
The angles of a triangle are 45°, 65°, and x°. What is x?
Which choice is correct?
A) 60°
B) 70°
C) 80°
D) 90°
Show full solution
Correct answer: B) 70°
The angles of a triangle sum to 180°. Therefore x=180-45-65=70°.
SAT trap: Always use the 180° angle sum for a triangle.
TRIANGLE BASICS
EASY
Question 2
Two angles of a triangle measure 38° and 72°. What is the third angle?
Which choice is correct?
A) 60°
B) 70°
C) 72°
D) 110°
Show full solution
Correct answer: B) 70°
The third angle is 180-38-72=70°.
SAT trap: Subtract both known angles from 180°.
TRIANGLE BASICS
EASY
Question 3
A triangle has side lengths 6, 8, and 10. Which classification is correct?
Which choice is correct?
A) Acute
B) Right
C) Obtuse
D) Equilateral
Show full solution
Correct answer: B) Right
Since 6²+8²=36+64=100=10², the triangle is right.
SAT trap: Use the longest side as c when checking the Pythagorean relationship.
TRIANGLE BASICS
EASY
Question 4
Which set of side lengths can form a triangle?
Which choice is correct?
A) 2, 3, 6
B) 4, 5, 8
C) 1, 2, 4
D) 3, 3, 7
Show full solution
Correct answer: B) 4, 5, 8
For a triangle, the sum of any two side lengths must exceed the third. Here 4+5>8.
SAT trap: Check the two smallest sides against the largest side.
TRIANGLE BASICS
EASY
Question 5
Which set cannot form a triangle?
Which choice is correct?
A) 5, 6, 8
B) 7, 7, 10
C) 3, 4, 7
D) 9, 10, 12
Show full solution
Correct answer: C) 3, 4, 7
Because 3+4=7, the sides form a straight line rather than a triangle.
SAT trap: The sum must be greater than the third side, not equal to it.
TRIANGLE BASICS
EASY
Question 6
A triangle has side lengths 5, 5, and 8. What type of triangle is it by side length?
Which choice is correct?
A) Scalene
B) Isosceles
C) Equilateral
D) Right
Show full solution
Correct answer: B) Isosceles
Two side lengths are equal, so the triangle is isosceles.
SAT trap: Classify by side length, not by angle.
TRIANGLE BASICS
EASY
Question 7
A triangle has side lengths 7, 9, and 11. What type of triangle is it by side length?
Which choice is correct?
A) Scalene
B) Isosceles
C) Equilateral
D) Right
Show full solution
Correct answer: A) Scalene
All three sides have different lengths.
SAT trap: Scalene means no equal sides.
TRIANGLE BASICS
EASY
Question 8
An equilateral triangle has a perimeter of 36. What is the length of each side?
Which choice is correct?
A) 6
B) 9
C) 12
D) 18
Show full solution
Correct answer: C) 12
All three sides are equal, so each side is 36/3=12.
SAT trap: Divide the perimeter by 3.
TRIANGLE BASICS
EASY
Question 9
A triangle has side lengths 9, 9, and 9. What is the measure of each angle?
Which choice is correct?
A) 45°
B) 60°
C) 90°
D) 120°
Show full solution
Correct answer: B) 60°
An equilateral triangle has three equal angles, each measuring 60°.
SAT trap: Equal sides in an equilateral triangle imply equal angles.
TRIANGLE BASICS
EASY
Question 10
What is the area of a triangle with base 12 and height 7?
Which choice is correct?
A) 42
B) 56
C) 84
D) 96
Show full solution
Correct answer: A) 42
Area=(1/2)(12)(7)=42.
SAT trap: Do not forget the factor of 1/2.
TRIANGLE BASICS
MEDIUM
Question 11
A triangle has area 30 and base 10. What is its height?
Which choice is correct?
A) 3
B) 6
C) 10
D) 12
Show full solution
Correct answer: B) 6
30=(1/2)(10)h=5h, so h=6.
SAT trap: Use perpendicular height, not a slanted side.
TRIANGLE BASICS
MEDIUM
Question 12
A triangle has a base of 15 and a height of 8. What is its area?
Which choice is correct?
A) 60
B) 90
C) 120
D) 180
Show full solution
Correct answer: A) 60
Area=(1/2)(15)(8)=60.
SAT trap: Multiply base and height, then divide by 2.
TRIANGLE BASICS
MEDIUM
Question 13
The perimeter of a triangle is 32. Two sides are 9 and 11. What is the third side?
Which choice is correct?
A) 10
B) 11
C) 12
D) 13
Show full solution
Correct answer: C) 12
The third side is 32-9-11=12.
SAT trap: Perimeter is the sum of all side lengths.
TRIANGLE BASICS
MEDIUM
Question 14
A triangle has angles 30°, 60°, and 90°. What type of triangle is it?
Which choice is correct?
A) Acute
B) Right
C) Obtuse
D) Equilateral
Show full solution
Correct answer: B) Right
It contains a 90° angle, so it is a right triangle.
SAT trap: Angle classification depends on the largest angle.
TRIANGLE BASICS
MEDIUM
Question 15
A triangle has angles 40°, 50°, and 90°. Which statement is true?
Which choice is correct?
A) It is acute
B) It is right
C) It is obtuse
D) It is equilateral
Show full solution
Correct answer: B) It is right
A triangle with one 90° angle is a right triangle.
SAT trap: Only one right angle is possible in a triangle.
Build Stronger SAT Geometry Skills
Connect triangle properties with equations, ratios, and real SAT Math timing.
How Are Angle Relationships, Isosceles Triangles, and Equilateral Triangles Tested?
These questions use equal-side properties, exterior angles, angle ratios, and side-angle comparisons.
ANGLE RELATIONSHIPS
MEDIUM
Question 16
In an isosceles triangle, the two equal sides are opposite angles of 52° and x°. What is x?
Which choice is correct?
A) 38°
B) 52°
C) 64°
D) 76°
Show full solution
Correct answer: B) 52°
Angles opposite equal sides are equal, so x=52°.
SAT trap: Match equal sides with their opposite angles.
ANGLE RELATIONSHIPS
MEDIUM
Question 17
An isosceles triangle has vertex angle 40°. What is each base angle?
Which choice is correct?
A) 40°
B) 60°
C) 70°
D) 80°
Show full solution
Correct answer: C) 70°
The two base angles are equal and sum to 140°, so each is 70°.
SAT trap: Subtract the vertex angle from 180°, then divide by 2.
ANGLE RELATIONSHIPS
MEDIUM
Question 18
An isosceles triangle has base angles of 65°. What is the vertex angle?
Which choice is correct?
A) 40°
B) 50°
C) 65°
D) 115°
Show full solution
Correct answer: B) 50°
The vertex angle is 180-65-65=50°.
SAT trap: Use both equal base angles.
ANGLE RELATIONSHIPS
MEDIUM
Question 19
An exterior angle of a triangle measures 120°. One remote interior angle is 45°. What is the other remote interior angle?
Which choice is correct?
A) 65°
B) 70°
C) 75°
D) 80°
Show full solution
Correct answer: C) 75°
An exterior angle equals the sum of the two remote interior angles: 120=45+x.
SAT trap: Do not add the adjacent interior angle.
ANGLE RELATIONSHIPS
MEDIUM
Question 20
An exterior angle measures 135°. The two remote interior angles are x° and 55°. What is x?
Which choice is correct?
A) 70°
B) 75°
C) 80°
D) 90°
Show full solution
Correct answer: C) 80°
135=x+55, so x=80°.
SAT trap: Use the exterior-angle theorem.
ANGLE RELATIONSHIPS
MEDIUM
Question 21
A triangle has interior angles x°, 2x°, and 3x°. What is x?
Which choice is correct?
A) 20°
B) 25°
C) 30°
D) 35°
Show full solution
Correct answer: C) 30°
x+2x+3x=180, so 6x=180 and x=30°.
SAT trap: Combine like terms before solving.
ANGLE RELATIONSHIPS
MEDIUM
Question 22
The angles of a triangle are x°, x°, and 4x°. What is the largest angle?
Which choice is correct?
A) 30°
B) 60°
C) 90°
D) 120°
Show full solution
Correct answer: D) 120°
6x=180, so x=30°. The largest angle is 4x=120°.
SAT trap: Find x before selecting the largest angle.
ANGLE RELATIONSHIPS
MEDIUM
Question 23
One angle of a triangle is twice another. The third angle is 60°. If the smaller of the first two angles is x°, what is x?
Which choice is correct?
A) 30°
B) 40°
C) 50°
D) 60°
Show full solution
Correct answer: B) 40°
x+2x+60=180, so 3x=120 and x=40°.
SAT trap: Translate ‘twice’ as 2x.
ANGLE RELATIONSHIPS
MEDIUM
Question 24
An isosceles triangle has equal sides of length 13 and base 10. An altitude is drawn to the base. What is the length of half the base?
Which choice is correct?
A) 5
B) 6
C) 10
D) 13
Show full solution
Correct answer: A) 5
In an isosceles triangle, the altitude from the vertex bisects the base, so half of 10 is 5.
SAT trap: The vertex altitude creates two congruent right triangles.
ANGLE RELATIONSHIPS
MEDIUM
Question 25
An equilateral triangle has side length 8. What is its perimeter?
Which choice is correct?
A) 16
B) 20
C) 24
D) 32
Show full solution
Correct answer: C) 24
Perimeter=3(8)=24.
SAT trap: All three sides are equal.
ANGLE RELATIONSHIPS
HARD
Question 26
An equilateral triangle has side length 6. What is its height?
Which choice is correct?
A) 3
B) 3√2
C) 3√3
D) 6√3
Show full solution
Correct answer: C) 3√3
The height of an equilateral triangle is s√3/2=6√3/2=3√3.
SAT trap: Use the 30-60-90 triangle relationship.
ANGLE RELATIONSHIPS
HARD
Question 27
An equilateral triangle has side length 10. What is its area?
Which choice is correct?
A) 25√3
B) 50
C) 50√3
D) 100√3
Show full solution
Correct answer: A) 25√3
Area=(√3/4)s²=(√3/4)(100)=25√3.
SAT trap: Use the equilateral-triangle area formula or base-height method.
ANGLE RELATIONSHIPS
HARD
Question 28
The sides opposite angles A and B in a triangle are 12 and 9, respectively. Which angle is larger?
Which choice is correct?
A) Angle A
B) Angle B
C) They are equal
D) Cannot be determined
Show full solution
Correct answer: A) Angle A
The larger side lies opposite the larger angle. Since 12>9, angle A is larger.
SAT trap: Compare each side with its opposite angle.
ANGLE RELATIONSHIPS
HARD
Question 29
In a triangle, angle X is larger than angle Y. Which statement must be true?
Which choice is correct?
A) The side opposite X is longer than the side opposite Y
B) The side opposite X is shorter
C) The two opposite sides are equal
D) The triangle is right
Show full solution
Correct answer: A) The side opposite X is longer than the side opposite Y
Larger angles are opposite longer sides.
SAT trap: Angle size and opposite side length have the same ordering.
ANGLE RELATIONSHIPS
HARD
Question 30
An exterior angle of a triangle is 150°, and one remote interior angle is 70°. What is the other remote interior angle?
Which choice is correct?
A) 70°
B) 80°
C) 90°
D) 100°
Show full solution
Correct answer: B) 80°
150=70+x, so x=80°.
SAT trap: The exterior angle equals the sum of the remote interior angles.
How Are Right and Special Triangles Tested?
These questions use the Pythagorean theorem, 45-45-90 triangles, 30-60-90 triangles, and geometric applications.
RIGHT AND SPECIAL TRIANGLES
MEDIUM
Question 31
A right triangle has legs 9 and 12. What is the hypotenuse?
Which choice is correct?
A) 13
B) 15
C) 18
D) 21
Show full solution
Correct answer: B) 15
c=√(9²+12²)=√225=15.
SAT trap: The hypotenuse is opposite the right angle.
RIGHT AND SPECIAL TRIANGLES
MEDIUM
Question 32
A right triangle has hypotenuse 13 and one leg 5. What is the other leg?
Which choice is correct?
A) 8
B) 10
C) 12
D) 18
Show full solution
Correct answer: C) 12
The missing leg is √(13²-5²)=√144=12.
SAT trap: Subtract the square of the known leg from the square of the hypotenuse.
RIGHT AND SPECIAL TRIANGLES
MEDIUM
Question 33
A right triangle has legs 7 and 24. What is the hypotenuse?
Which choice is correct?
A) 25
B) 26
C) 28
D) 31
Show full solution
Correct answer: A) 25
7²+24²=49+576=625=25².
SAT trap: Recognize common Pythagorean triples.
RIGHT AND SPECIAL TRIANGLES
MEDIUM
Question 34
A right triangle has hypotenuse 17 and one leg 8. What is the other leg?
Which choice is correct?
A) 9
B) 12
C) 15
D) 16
Show full solution
Correct answer: C) 15
17²-8²=289-64=225, so the other leg is 15.
SAT trap: Take the square root after subtracting squares.
RIGHT AND SPECIAL TRIANGLES
MEDIUM
Question 35
A 45-45-90 triangle has a leg of length 6. What is the hypotenuse?
Which choice is correct?
A) 6√2
B) 12
C) 12√2
D) 18
Show full solution
Correct answer: A) 6√2
In a 45-45-90 triangle, hypotenuse=leg√2.
SAT trap: Do not double the leg.
RIGHT AND SPECIAL TRIANGLES
MEDIUM
Question 36
A 45-45-90 triangle has hypotenuse 10√2. What is each leg?
Which choice is correct?
A) 5
B) 10
C) 10√2
D) 20
Show full solution
Correct answer: B) 10
Since hypotenuse=leg√2, the leg is 10.
SAT trap: Divide the hypotenuse by √2.
RIGHT AND SPECIAL TRIANGLES
MEDIUM
Question 37
A 30-60-90 triangle has short leg 5. What is the hypotenuse?
Which choice is correct?
A) 5√2
B) 5√3
C) 10
D) 10√3
Show full solution
Correct answer: C) 10
In a 30-60-90 triangle, hypotenuse=2(short leg).
SAT trap: Identify the side opposite 30° as the short leg.
RIGHT AND SPECIAL TRIANGLES
MEDIUM
Question 38
A 30-60-90 triangle has short leg 4. What is the long leg?
Which choice is correct?
A) 4√2
B) 4√3
C) 8
D) 8√3
Show full solution
Correct answer: B) 4√3
The long leg equals short leg times √3.
SAT trap: Do not confuse the long leg with the hypotenuse.
RIGHT AND SPECIAL TRIANGLES
MEDIUM
Question 39
A 30-60-90 triangle has hypotenuse 18. What is the short leg?
Which choice is correct?
A) 6
B) 9
C) 9√3
D) 18√3
Show full solution
Correct answer: B) 9
The short leg is half the hypotenuse.
SAT trap: Use the 1:√3:2 ratio.
RIGHT AND SPECIAL TRIANGLES
MEDIUM
Question 40
A right triangle has legs 10 and 24. What is its area?
Which choice is correct?
A) 60
B) 120
C) 240
D) 260
Show full solution
Correct answer: B) 120
The legs are perpendicular, so area=(1/2)(10)(24)=120.
SAT trap: For a right triangle, the legs can serve as base and height.
RIGHT AND SPECIAL TRIANGLES
HARD
Question 41
A right triangle has hypotenuse 25 and one leg 15. What is the other leg?
Which choice is correct?
A) 10
B) 18
C) 20
D) 22
Show full solution
Correct answer: C) 20
25²-15²=625-225=400, so the missing leg is 20.
SAT trap: Use the Pythagorean theorem with the hypotenuse as c.
RIGHT AND SPECIAL TRIANGLES
HARD
Question 42
A square has diagonal 8√2. What is the side length?
Which choice is correct?
A) 4
B) 8
C) 8√2
D) 16
Show full solution
Correct answer: B) 8
The diagonal of a square forms a 45-45-90 triangle, so diagonal=side√2.
SAT trap: Use the special-triangle relationship.
RIGHT AND SPECIAL TRIANGLES
HARD
Question 43
A rectangle has side lengths 6 and 8. What is the length of its diagonal?
Which choice is correct?
A) 10
B) 12
C) 14
D) 48
Show full solution
Correct answer: A) 10
The diagonal is the hypotenuse of a right triangle: √(6²+8²)=10.
SAT trap: Do not add the side lengths.
RIGHT AND SPECIAL TRIANGLES
HARD
Question 44
A right triangle has a leg of 12 and hypotenuse 20. What is the other leg?
Which choice is correct?
A) 8
B) 12
C) 16
D) 18
Show full solution
Correct answer: C) 16
20²-12²=400-144=256, and √256=16.
SAT trap: Square first, then subtract.
RIGHT AND SPECIAL TRIANGLES
HARD
Question 45
A ladder 13 feet long reaches 12 feet up a wall. How far is the foot of the ladder from the wall?
Which choice is correct?
A) 5 feet
B) 7 feet
C) 12 feet
D) 25 feet
Show full solution
Correct answer: A) 5 feet
The ladder is the hypotenuse: distance=√(13²-12²)=5.
SAT trap: Model the wall, ground, and ladder as a right triangle.
Practice More SAT Geometry and Trigonometry
Build accuracy with right triangles, special triangles, and geometry applications.
How Are Similarity and Congruence Tested?
These questions use proportional sides, perimeter scale factors, area scale factors, and triangle congruence conditions.
SIMILARITY AND CONGRUENCE
HARD
Question 46
Two similar triangles have corresponding sides 6 and 9. If another side of the smaller triangle is 10, what is the corresponding side of the larger triangle?
Which choice is correct?
A) 12
B) 15
C) 18
D) 24
Show full solution
Correct answer: B) 15
The scale factor is 9/6=3/2, so the corresponding side is 10(3/2)=15.
SAT trap: Apply the same scale factor to corresponding sides.
SIMILARITY AND CONGRUENCE
HARD
Question 47
Two similar triangles have a scale factor of 4 from small to large. If the small triangle’s area is 12, what is the large triangle’s area?
Which choice is correct?
A) 48
B) 96
C) 192
D) 256
Show full solution
Correct answer: C) 192
Areas scale by the square of the side scale factor: 12(4²)=192.
SAT trap: Area does not scale linearly with side length.
SIMILARITY AND CONGRUENCE
HARD
Question 48
Two similar triangles have corresponding sides 8 and 12. What is the scale factor from the first triangle to the second?
Which choice is correct?
A) 2/3
B) 3/2
C) 4
D) 20
Show full solution
Correct answer: B) 3/2
The scale factor is 12/8=3/2.
SAT trap: Keep the direction of the scale factor clear.
SIMILARITY AND CONGRUENCE
HARD
Question 49
A triangle with sides 3, 4, and 5 is similar to a triangle whose shortest side is 9. What is the longest side of the larger triangle?
Which choice is correct?
A) 12
B) 15
C) 18
D) 27
Show full solution
Correct answer: B) 15
The scale factor is 9/3=3, so the longest side is 5(3)=15.
SAT trap: Match shortest to shortest and longest to longest.
SIMILARITY AND CONGRUENCE
HARD
Question 50
Which condition is sufficient to prove two triangles similar?
Which choice is correct?
A) AA
B) One equal side
C) Equal perimeters
D) Equal areas only
Show full solution
Correct answer: A) AA
If two pairs of corresponding angles are equal, the triangles are similar.
SAT trap: One matching angle is not enough.
SIMILARITY AND CONGRUENCE
HARD
Question 51
Which condition can prove two triangles congruent?
Which choice is correct?
A) SSS
B) AAA
C) Equal area only
D) One equal angle
Show full solution
Correct answer: A) SSS
Three pairs of equal corresponding sides establish congruence.
SAT trap: AAA proves similarity, not congruence.
SIMILARITY AND CONGRUENCE
HARD
Question 52
Two triangles have side lengths 5, 7, 9 and 10, 14, 18. Which statement is true?
Which choice is correct?
A) They are congruent
B) They are similar with scale factor 2
C) They are not related
D) Their areas are equal
Show full solution
Correct answer: B) They are similar with scale factor 2
Each side in the second triangle is twice the corresponding side in the first.
SAT trap: Proportional sides indicate similarity.
SIMILARITY AND CONGRUENCE
HARD
Question 53
Two similar triangles have perimeters 18 and 30. If a side of the smaller triangle is 6, what is the corresponding side of the larger triangle?
Which choice is correct?
A) 8
B) 10
C) 12
D) 15
Show full solution
Correct answer: B) 10
The scale factor is 30/18=5/3, so 6(5/3)=10.
SAT trap: Perimeters scale by the same factor as side lengths.
SIMILARITY AND CONGRUENCE
HARD
Question 54
A triangle is enlarged by a scale factor of 3. Its original area is 20. What is the new area?
Which choice is correct?
A) 60
B) 120
C) 180
D) 540
Show full solution
Correct answer: C) 180
Area scales by 3²=9, so 20(9)=180.
SAT trap: Square the side scale factor for area.
SIMILARITY AND CONGRUENCE
HARD
Question 55
Two right triangles each have a hypotenuse of 10 and a leg of 6. Which theorem proves them congruent?
Which choice is correct?
A) HL
B) AA
C) AAA
D) SSA only
Show full solution
Correct answer: A) HL
For right triangles, a congruent hypotenuse and one congruent leg establish congruence.
SAT trap: HL applies only to right triangles.
What Do Hard Mixed Triangle Questions Look Like?
These questions combine algebra, altitude construction, area, similarity, and special-triangle relationships.
HARD MIXED TRIANGLES
HARD
Question 56
A triangle has sides x, x+2, and x+4 with perimeter 30. What is x?
Which choice is correct?
A) 6
B) 8
C) 10
D) 12
Show full solution
Correct answer: B) 8
3x+6=30, so 3x=24 and x=8.
SAT trap: Write the perimeter equation before solving.
HARD MIXED TRIANGLES
HARD
Question 57
An isosceles triangle has equal sides 10 and base 12. What is its height?
Which choice is correct?
A) 6
B) 8
C) 10
D) 12
Show full solution
Correct answer: B) 8
The altitude bisects the base into 6 and 6. Then h=√(10²-6²)=8.
SAT trap: Use the altitude to form two right triangles.
HARD MIXED TRIANGLES
HARD
Question 58
An isosceles triangle has equal sides 13 and base 10. What is its area?
Which choice is correct?
A) 50
B) 60
C) 65
D) 120
Show full solution
Correct answer: B) 60
The altitude bisects the base into 5 and 5. Height=√(13²-5²)=12, so area=(1/2)(10)(12)=60.
SAT trap: Find the height before using the area formula.
HARD MIXED TRIANGLES
HARD
Question 59
A right triangle has legs x and x+7 and hypotenuse 17. What is x?
Which choice is correct?
A) 6
B) 8
C) 10
D) 12
Show full solution
Correct answer: B) 8
x²+(x+7)²=17². This gives 2x²+14x-240=0, or x²+7x-120=0=(x+15)(x-8). Thus x=8.
SAT trap: Reject negative side lengths.
HARD MIXED TRIANGLES
HARD
Question 60
A 30-60-90 triangle has long leg 12√3. What is the short leg?
Which choice is correct?
A) 6
B) 12
C) 18
D) 24
Show full solution
Correct answer: B) 12
The long leg equals short leg times √3, so the short leg is 12.
SAT trap: Divide by √3.
HARD MIXED TRIANGLES
HARD
Question 61
A 45-45-90 triangle has area 32. What is the length of each leg?
Which choice is correct?
A) 4
B) 8
C) 8√2
D) 16
Show full solution
Correct answer: B) 8
If each leg is x, then area=(1/2)x²=32, so x²=64 and x=8.
SAT trap: The equal legs are perpendicular.
HARD MIXED TRIANGLES
HARD
Question 62
Two similar triangles have side scale factor 5/2. If the smaller area is 24, what is the larger area?
Which choice is correct?
A) 60
B) 100
C) 150
D) 300
Show full solution
Correct answer: C) 150
Area scale factor=(5/2)²=25/4. Then 24(25/4)=150.
SAT trap: Square the side scale factor.
HARD MIXED TRIANGLES
HARD
Question 63
A triangle has side lengths 7, 24, and 25. What is its area?
Which choice is correct?
A) 84
B) 168
C) 175
D) 300
Show full solution
Correct answer: A) 84
Since 7²+24²=25², the triangle is right. Area=(1/2)(7)(24)=84.
SAT trap: Recognize the right triangle before finding area.
HARD MIXED TRIANGLES
HARD
Question 64
A triangle has sides 5, 12, and 13. A similar triangle has area 150. If the original area is 30, what is the side scale factor?
Which choice is correct?
A) √5
B) 5
C) 10
D) 25
Show full solution
Correct answer: A) √5
The area scale factor is 150/30=5, so the side scale factor is √5.
SAT trap: Take the square root of the area ratio.
HARD MIXED TRIANGLES
HARD
Question 65
A triangle has angles in the ratio 2:3:4. What is the largest angle?
Which choice is correct?
A) 40°
B) 60°
C) 80°
D) 100°
Show full solution
Correct answer: C) 80°
The ratio parts total 9, so each part is 20°. The largest angle is 4(20)=80°.
SAT trap: Convert the ratio into angle measures using 180°.
What Do Student-Produced Response Questions Look Like?
Enter the requested angle, side length, hypotenuse, or area.
STUDENT-PRODUCED RESPONSE
MEDIUM
Question 66
The angles of a triangle are 35°, 65°, and x°. What is x?
Enter your answer.
Show full solution
Correct answer: 80
180-35-65=80.
SAT trap: Enter only the requested numerical value.
STUDENT-PRODUCED RESPONSE
MEDIUM
Question 67
A right triangle has legs 5 and 12. What is the hypotenuse?
Enter your answer.
Show full solution
Correct answer: 13
5²+12²=13².
SAT trap: Enter only the requested numerical value.
STUDENT-PRODUCED RESPONSE
MEDIUM
Question 68
An equilateral triangle has perimeter 45. What is one side length?
Enter your answer.
Show full solution
Correct answer: 15
45/3=15.
SAT trap: Enter only the requested numerical value.
STUDENT-PRODUCED RESPONSE
MEDIUM
Question 69
A triangle has base 14 and height 9. What is its area?
Enter your answer.
Show full solution
Correct answer: 63
(1/2)(14)(9)=63.
SAT trap: Enter only the requested numerical value.
STUDENT-PRODUCED RESPONSE
MEDIUM
Question 70
A 30-60-90 triangle has hypotenuse 20. What is the short leg?
Enter your answer.
Show full solution
Correct answer: 10
The short leg is half the hypotenuse.
SAT trap: Enter only the requested numerical value.
Common SAT Triangle Mistakes
| Mistake | Correction |
|---|---|
| Forgetting the 180° angle sum | Add all interior angles and set the total equal to 180° |
| Using the wrong side as the hypotenuse | Use the side opposite the right angle |
| Confusing special-triangle ratios | Memorize 1:1:√2 and 1:√3:2 |
| Scaling area linearly | Area scales by the square of the side scale factor |
Two-Week SAT Triangles Study Plan
| Days | Focus |
|---|---|
| 1-3 | Q1-Q15: triangle basics, perimeter, and area |
| 4-6 | Q16-Q30: angle relationships and isosceles properties |
| 7-10 | Q31-Q45: right and special triangles |
| 11-12 | Q46-Q55: similarity and congruence |
| 13-14 | Q56-Q70 and error review |
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