AIME Geometry 2

Question 1

The diagonals of a rhombus are 10 and 24. Find its perimeter.

Accepted Answer

52

Answer

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?

Accepted Answer

60°

Answer

Angles sum to 180°: C=180-50-70=60°.

Question 3

A cone has base radius 3 and height 4. Find its slant height.

Accepted Answer

5

Answer

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?

Accepted Answer

9:25

Answer

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.

Accepted Answer

0

Answer

Distance = |3(1)-4(2)+5|/√(9+16)=|3-8+5|/5=|0|/5=0.

AIME - American Invitational Mathematics Examination Practice Test