The top of a 15-foot ladder is 3 ft. father 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?

Question

The top of a 15-foot ladder is 3 ft. father 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?

drwls · Accepted Answer

Let x be the distance of the foot from the wall. Then use the Pythagorean theorem.
x^2 + (x+3)^2 = 15^2 = 225
2x^2 +6x -216 = 0
x^2 +3x -108 = 0
That factors easily. (Think: 9x12 = 108)Take the positive root.