Question

A ladder is leaning against a wall. The top of the ladder is 9 feet (ft) above the ground. If the bottom of the ladder is moved 3ft farther from the wall, the ladder will be lying flat on the ground, still touching the wall. How long, in feet, is the ladder?

Answer 1

Step 1

First situation

when a ladder is leaning against a wall

Let

x-------> the distance of the bottom of the ladder from the wall

L-------> the length of the ladder

Find the length of the ladder

Applying the Pythagorean Theorem

$L^{2} =x^{2}+ 9^{2}$ ------> equation $1$

Step 2

Second situation

when the ladder will be lying flat on the ground

Find the length of the ladder

In this situation the length of the ladder is equal to

$L=x+3$

square both sides

$L^{2}=(x+3)^{2}$ ------> equation $2$

Step 3

equate equation $1$ and equation $2$

$x^{2}+ 9^{2}=(x+3)^{2}\\x^{2}+81=x^{2} +6x+9\\ 6x=81-9\\6x=72\\x=12\ ft$

therefore

the answer is

the length of the ladder is $12\ ft$

see the attached figure to better understand the problem