Ladder problem for algebra 2

Question

The top of a 15-foot ladder is 3 ft farther up a wall than the foot of the ladder is from the bottom of the wall. How far is the foot of the ladder from the bottom of the wall?

Answer 1

You have a right triangle with

 

hypotenuse = 15

base = x = distance from foot of the ladder to bottom of the wall

height = x + 3

 

x² + (x + 3)² = 15²

 

x² + (x² + 6x + 9) = 225

 

2x² + 6x - 216 = 0

 

x² + 3x - 108 = 0

 

(x + 12)(x - 9) = 0

 

x = 9 ft