Question

A ladder is leaning against a building so that the distance from the ground to the top of the ladder is 3 feet less than the length of the ladder. Find the length of the ladder if the distance from the bottom of the ladder to the building is 9 feet.

Answer 1

15 ft

Explanation:

This is another classic case of Pythagoras theorem. To start with, let's assume that the length of the ladder we're looking for is x

We're told that the height of the building the ladder is leaning on is, x - 3

Also we're told that the distance at an adjacent from the ladder is 9 ft.

If we use Pythagoras theorem, we have

x² = (x - 3)² + 9²

x² = x² - 6x + 9 + 81

On rearranging, we have

x² - x² = -6x + 90

6x = 90

x = 90 / 6

x = 15 ft

Therefore, the length of the ladder is found to be 15 ft