SOLUTION: A ladder is leaning against a building. The distance from the bottom of the ladder to the building is 6 ft shorter than the length of the ladder. How high up the side of the buildi

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Question 1040926: A ladder is leaning against a building. The distance from the bottom of the ladder to the building is 6 ft shorter than the length of the ladder. How high up the side of the building is the top of the ladder if that distance is 3 ft less than the length of the ladder?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39613) (Show Source):
You can put this solution on YOUR website!
hypotenuse, same as the ladder, h
leg on the wall, h-6
leg on the ground, h-3

Pythagorean Theorem Relationship because Right Triangle:

One root makes sense and the other root makes no sense.

Answer by MathTherapy(10549) (Show Source):
You can put this solution on YOUR website!

A ladder is leaning against a building. The distance from the bottom of the ladder to the building is 6 ft shorter than the length of the ladder. How high up the side of the building is the top of the ladder if that distance is 3 ft less than the length of the ladder?

Let height up the wall that the ladder rests, be H
Then height of ladder (hypotenuse of right triangle formed) = H + 3, and distance from bottom of ladder to base of building = H + 3 - 6, or H - 3
We then get:

H(H - 12) = 0
H - 12 = 0 OR H = 0 (ignore)
H, or height up the wall that the ladder rests =