1950 AMC 12 Problem 32

Question

A

25

foot ladder is placed against a vertical wall of a building. The foot of the ladder is

7

feet from the base of the building. If the top of the ladder slips

4

feet, then the foot of the ladder will slide:

9

ft

15

ft

5

ft

8

ft

4

ft

Find the ladder’s original height on the wall using a right triangle

After the top slips, the new height is

4

feet less while the hypotenuse stays

25

The initial height, in feet, is

\sqrt{25^2-7^2}=\sqrt{576}=24.

After the top slips, the height is

20

feet, so the new horizontal distance is

\sqrt{25^2-20^2}=15

feet. The foot therefore slides

15-7=8

feet.

Thus, the correct answer is D.

Problem 32 in other years