Math question for Algebra

Question

A 13ft ladder rests against the side of a house. The distance between the top of the ladder and the ground is 7ft more than the distance between the base of the ladder and the bottom of the house. Find both distances.

I know i have: 13 Ft, X and X+7

how do i find the distance from the bottom of the ladder to the house and The distance from the top of the ladder to the ground? I get half way through and get stuck. Thank you!

Answer 1

pythagorean theorem

(x+7)^2= 13^2-x^2

expand

x^2+14x+49=169-x^2

combine like terms

2x^2+14x-120=0

divide by 2

x^2+7x-60=0

factor

(x-5)(x+12)

set 1st factor=0

x-5=0

x=5 feet from ladder bottom to house bottom

x+7=5+7= 12 feet from ladder top to house bottom