SOLUTION: One leg of a right triangle is 2cm longer than the other leg and 2 cm shorter than the hypotenuse. What is the length of each side? pls. help

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Question 511717: One leg of a right triangle is 2cm longer than the other leg and 2 cm shorter than the hypotenuse. What is the length of each side? pls. help
Answer by nerdybill(7384) About Me  (Show Source):
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One leg of a right triangle is 2cm longer than the other leg and 2 cm shorter than the hypotenuse. What is the length of each side?
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Let x = length of short leg
then
x+2 = length of long leg
x+2+2 = x+4 = length of hypotenuse
.
applying pythagorean:
x^2 + (x+2)^2 = (x+4)^2
x^2 + (x+2)(x+2) = (x+4)(x+4)
x^2 + x^2+4x+4 = x^2+8x+16
2x^2+4x+4 = x^2+8x+16
x^2+4x+4 = 8x+16
x^2-4x+4 = 16
x^2-4x-12 = 0
(x-6)(x+2) = 0
x = {-2,6}
throw out negative solution (extraneous) leaving
x = 6 cm (short leg)
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Long leg:
x+2 = 6+2 = 8 cm
.
hypotenuse:
x+4 = 6+4 = 10 cm