Question

A 13 foot ladder is leaning against a vertical wall. The distance from the top of the ladder to the bottom of the wall is 7 feet longer than the distance from the bottom of the ladder to the bottom of the wall. Find how high the top of the ladder reacher on the side of the wall.

Answer 1

a= x
b = x+7
c = 13

x^2 + (x+7)^2 = 13^2
= x^2 + x^2 +7x +7x + 49 = 169
= 2x^2 + 14x + 49 = 169
= 2x^2 + 14x + 49 -169= 169-169
= 2x^2 + 14x -120 = 0
= x^2 +7x -60 = 0
(x -5)(x+12)= 0

x = 5
x = -12 ignored when it is negative

a= 5
b = 12