Find the length of the ladder if the length is 2 ft more than its distance from the wall.

Question

A ladder is resting against a wall. The top of the ladder touches the wall at a height of 6 feet. Find the length of the ladder if the length is two feet more than its distance from the wall.

Answer 1

the ladder, the wall, and the ground distance form a right triangle where the ladder is the hypotenuse

x=distance from the wall

x+2=length of the ladder

(x+2)²=6²+x² using the Pythagorean Theorem

x²+4x+4=36+x²

subtract x² from both sides

4x+4=36

4x=36-4

4x=32

x=32/4

x=8 feet

x+2=10 feet is the length of the ladder