Answer:
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
