SOLUTION: A ladder is leaning agains ta building. The distance from the bottom of the ladder to the building is 2 ft shorter than the length of the ladder. How high up the side of the buil

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Question 628915: A ladder is leaning agains ta building. The distance from the bottom of the ladder to the building is 2 ft shorter than the length of the ladder. How high up the side of the building is the top of the ladder if the distance is 1 ft less than the length of the ladder?
Answer by lwsshak3(11628) (Show Source):
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A ladder is leaning agains a building. The distance from the bottom of the ladder to the building is 2 ft shorter than the length of the ladder. How high up the side of the building is the top of the ladder if the distance is 1 ft less than the length of the ladder?
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let x= length of ladder
x-2=distance from bottom of ladder to bldg
x-1=How high up the side of the building is the top of the ladder
This makes for a right triangle with legs, (x-1), (x-2) and hypotenuse x.
..
By Pythagorean Theorem:
x^2=(x-1)^2+(x-2)^2
x^2=(x^2-2x+1)+(x^2-4x+4)
x^2=2x^2-6x+5
x^2-6x+5=0
(x-5)(x-1)=0
x=1 (reject, not reasonable)
or
x=5
x-1=4
How high up the side of the building is the top of the ladder: 4 ft