SOLUTION: the lengths of the three sides of a right triangle are represented by consecutive even whole numbers. find the lengths of the three sides.

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Question 171123: the lengths of the three sides of a right triangle are represented by consecutive even whole numbers. find the lengths of the three sides.
Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!
.
Let ---> system%28x=opposite%2Cx%2B2=adjacent%2Cx%2B4=hypotenuse%29
Then by Pyth Theorem:
%28x%2B4%29%5E2=x%5E2%2B%28x%2B2%29%5E2, Expand
x%5E2%2B8x%2B16x=x%5E2%2Bx%5E2%2B4x%2B4}
8x%2B16-4x-4=x%5E2%2Bcross%28x%5E2%29-cross%28x%5E2%29
4x%2B12=x%5E2
x%5E2-4x-12=0, Perfect square,
%28x-6%29%28x%2B2%29=0
highlight%28x=6%29, opposite side: x=-2, disregard
x%2B2=6%2B2=highlight%288%29, adjacent side
x%2B4=6%2B4=highlight%2810%29,hypotenuse
Consecutive even whole numbers ----->system%28opp=6%2Cadj=8%2Chyp=10%29
Thank you,
Jojo