SOLUTION: The legs of a right triangle differ by 2 centimeters and the hypotenuse is 4 centimeters more than the shorter leg. Find the sides of the triangle.

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Question 165934: The legs of a right triangle differ by 2 centimeters and the hypotenuse is 4 centimeters more than the shorter leg. Find the sides of the triangle.
Answer by jojo14344(1512) About Me  (Show Source):
You can put this solution on YOUR website!
shorter_leg=x ---> let's point it as the adjacent side
x%2B2 -------------> let's point it as the oppposite side
x%2B4 -------------> hypotenuse side
differ by 2cm --system%28x=adj%2Cx%2B2=opp%29
By Pyth. Theorem:
%28x%2B4%29%5E2=x%5E2%2B%28x%2B2%29%5E2
x%5E2%2B8x%2B16=x%5E2%2Bx%5E2%2B4x%2B4
2x%5E2%2B4x%2B4-x%5E2-8x-16=0
x%5E2-4x-12=0, perfect square, factorable
%28x-6%29%28x%2B2%29=0
2 values ---system%28highlight%28x=6%29%2Cx=-2%29
As highlighted, shortest side: adj= 6cm; opp=6+2=8cm; hyp=6+4=10cm
See below,
drawing%28300%2C300%2C-5%2C10%2C-5%2C10%2Cgraph%28300%2C300%2C-5%2C10%2C-5%2C10%29%2C%28green%28line%286%2C0%2C0%2C0%29%29%29%2C%28blue%28line%286%2C0%2C6%2C8%29%29%29%2C%28red%28line%286%2C8%2C0%2C0%29%29%29%29 system%28green=adjacent=6cm%2Cblue=opposite=8cm%2Cred=hypotenuse=10cm%29
check:
10%5E2=6%5E2%2B8%5E2
100=36%2B64
100=100
Thank you,
Jojo