A fifteen foot long ladder is leaned against a wall so that the distance it reaches up the wall is 3 feet more than the distance between the base of the ladder and the wall. How far up the wall does the ladder reach?

Step-by-step explanation:

The ladder forms a right angle triangle with the wall and the ground. The length of the ladder represents the hypotenuse of the right angle triangle. The height from the top of the ladder to the base of the wall represents the opposite side of the right angle triangle.

The distance,h from the bottom of the ladder to the base of the wall represents the adjacent side of the right angle triangle.

If the distance that the ladder reaches up the wall is 3 feet more than the distance between the base of the ladder and the wall, h feet, then the distance that the ladder reaches up the wall is is (h + 3) feet

We would apply Pythagoras theorem which is expressed as

Hypotenuse² = opposite side² + adjacent side²

Therefore,

15² = (h + 3)² + h²

225 = (h + 3)(h + 3) + h²

225 = h² + 3h + 3h + 9 + h²

2h² + 6h + 9 - 225 = 0

2h² + 6h - 216 = 0

Dividing through by 2, it becomes

h² + 3h - 108 = 0

h² + 12h - 9h - 108 = 0

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

h - 9 = 0 or h + 12 = 0

h = 9 or h = - 12

Since the distance cannot be negative, then h = 6

The distance of the top of the ladder from the base is

h + 3 = 6 + 3 = 9 feet