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 lenght is 2 feet more than its distance from the wall.

Answer 1

A rt. triangle is formed:

X Ft. = hor. side.
6 Ft. = ver. side.
(x+2) Ft. = hyp.

x^2 + 6^2 = (x+2)^2.
x^2 + 36 = x^2 + 4x + 4.
x^2 - x^2 + 4x + 4 = 36.
4x + 4 = 36.
4x = 36 - 4 = 32.

X = 32 / 4 = 8. Ft.
X+2 = 8 + 2 = 10 Ft .