Question

A ladder is resting against the wall. The top of the ladder touches the wall at a height of 12 feet. Find the distance from the wall to the bottom of the ladder and the length of the ladder, if the length of the ladder is 3 foot more than 2 times its distance from the wall.

Answer 1

Let d be the distance from the wall

`{12}^(2) = {(2d + 3)}^(2) - {d}^(2) \\ 144 = {4d}^(2) + 12d + 9 - {d}^(2) \\ 3d ^(2) + 12d - 135 = 0 \\ d = 5 \: or \: - 9(rej)`
Length of the ladder=2x5+3=13 feet