AIME Geometry 2 — Questions and Answers
Question 1: The diagonals of a rhombus are 10 and 24. Find its perimeter.
- 52 (Correct answer)
- 48
- 56
- 60
Correct answer: 52
Each side = √(5^2+12^2)=√169=13; perimeter=4×13=52.
Question 2: In triangle ABC, angle A = 50° and angle B = 70°. What is angle C?
- 60° (Correct answer)
- 70°
- 50°
- 80°
Correct answer: 60°
Angles sum to 180°: C=180-50-70=60°.
Question 3: A cone has base radius 3 and height 4. Find its slant height.
- 5 (Correct answer)
- 7
- √7
- √25
Correct answer: 5
Slant height = √(r^2+h^2)=√(9+16)=√25=5.
Question 4: Two similar triangles have corresponding sides in ratio 3:5. What is the ratio of their areas?
- 9:25 (Correct answer)
- 3:5
- 6:10
- 27:125
Correct answer: 9:25
The ratio of areas equals the square of the ratio of corresponding sides: (3/5)^2=9/25.
Question 5: Find the distance from point (1, 2) to the line 3x - 4y + 5 = 0.
- 0 (Correct answer)
- 1
- 2
- 3
Correct answer: 0
Distance = |3(1)-4(2)+5|/√(9+16)=|3-8+5|/5=|0|/5=0.
Question 6: What is the sum of interior angles of a hexagon?
- 720° (Correct answer)
- 540°
- 900°
- 360°
Correct answer: 720°
Sum = (n-2)×180°=(6-2)×180°=720°.
AIME Geometry 2
The diagonals of a rhombus are 10 and 24.
Find its perimeter.