A 13-ft ladder is leaning against a house. its base is "(x-7)" and perpendicular is "(x)".how far is the bottom of the ladder from the house.

Question

A 13-ft ladder is leaning against a house. the distance from the bottom of the ladder to the house is 7-ft less than the distance from the top of the ladder to the ground .how far is the bottom of the ladder from the house.

Answer 1

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

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

2x^2 -14x -120 = 0

x^2 -7x- 60 =0

(x-12)(x+5) = 0

x =12 feet

x-7= 5 feet from the bottom of the ladder to the house

the ladder forms a 5-12-13 right triangle

5^2 +12^2 = 13^2

25+144= 169