Question

The base of a ladder of length (x + 8) feet is positioned x feet from a wall and is leaning on the wall. The ladder reaches a height of (x + 7) feet along the wall. Find x

Answer 1

5

Explanation:

use the pythagorean theorem where
`c^(2) = a^2 + b^2`

c = x+8

a = x

b = x+7

`(x+8)^2 = x^2 + (x+7)^2`

`x^2 + 16x + 64 = x^2 + x^2 + 14x + 49`

`x^2 + 16x + 64 = 2x^2 +14x + 49`

`0=x^2-2x-15`

(x-5)(x+3)=0

x-5=0 or. x+3=0

x=5 or x=-3

x can not be negative so the answer is 5