SOLUTION: A ladder is leaning against a building. The distance from the bottom of the ladder to the buiding is 9 feet less than the length of the ladder. How high up the side of the building

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Question 887393: A ladder is leaning against a building. The distance from the bottom of the ladder to the buiding is 9 feet less than the length of the ladder. How high up the side of the building is the top of the ladder if that distance is 2 feet less than the length of the ladder?
Answer by lwsshak3(11628) About Me  (Show Source):
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A ladder is leaning against a building. The distance from the bottom of the ladder to the buiding is 9 feet less than the length of the ladder. How high up the side of the building is the top of the ladder if that distance is 2 feet less than the length of the ladder?
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let x=length of the ladder
x-9=distance from the bottom of the ladder to the building
x-2=How high up the side of the building is the top of the ladder
..
by the pythagorean theorem:
x^2=(x-9)^2+(x-2)^2
x^2=x^2-18x+81+x^2-4x+4
x^2=2x^2-22x+85
x^2-22x+85=0
(x-5)(x-17)=0
x=5 (reject)
or
x=17
x-2=15
How high up the side of the building is the top of the ladder? 15 ft