Question

A ladder is leaning against a wall. The top of the ladder is 9ft 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

By the pythagorean theorem:

L^2=9^2+x^2

and we are told if:

L^2=(x+3)^2

L=x+3

L-3=x now using this in our first equation L^2=9^2+x^2 we get

L^2=9^2+(L-3)^2

L^2=81+L^2-6L+9

0=90-6L

6L=90

L=15 ft