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A ladder is leaning against a building. the distance from the bottom of the ladder to the building is 16 ft shorter than the length of the ladder. how high up side of the building is the top of the ladder if the distance is 8 ft less

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randgh

 Pythagorean right triangle 

a^2 + b^2 = c^2

Let the length of the ladder be x.
One side is x - 16.
The other side is x - 8.


(x-16)^2 + (x-8)^2 = x^2

x^2 - 32x + 256 + x^2- 16 x+64 = x^2

x^2  - 48 x + 320 = 0

 ( x- 40 ) (x-8) = 0

x = 40  or x= 8 

we discard the second so x = 40 

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