algebra

Please show solution to this problem.

In triangle A, the longer leg is 6 more than the shorter leg and the hypotenuse is 6 more than the longer leg.

Find the lengths of each side of this right triangle. Show all calculations.

Short leg = _______ Long leg = ______ Hypotenuse = _________

Thank you.

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1. x^2 + (x+6)^2 = (x+12)^2

x^2+ x^2+ 12 x + 36 = x^2 +24 x +144

x^2 - 12 x - 108 = 0
108 is 6*18 for example
(x-18)(x+6) = 0
try x = 18
then x+6 = 24
and x+12 = 30
=====================
check
18^2 + 24^2 = 30^2 ????????
324 + 576 = 900 whew !

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