SOLUTION: In a right triangle, the length of the longer side is two more than twice the length of the shorter leg. The length of the hypotenuse is 8 more than the length of the shorter leg.

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Question 136992: In a right triangle, the length of the longer side is two more than twice the length of the shorter leg. The length of the hypotenuse is 8 more than the length of the shorter leg. Find the lengths of the sides of the triangle.
Answer by stanbon(75887) (Show Source):
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In a right triangle, the length of the longer side is two more than twice the length of the shorter leg. The length of the hypotenuse is 8 more than the length of the shorter leg. Find the lengths of the sides of the triangle.
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Let the shorter leg length be "x"
Then longer leg length is "2x+2"
And hypotenuse length = "x+8"
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EQUATION:
x^2 + (2x+2)^2 = (x+8)^2
x^2 + 4x^2+8x + 4 = x^2+16x+64
5x^2+8x + 4 = x^2+16x + 64
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4x^2 -8x - 60 = 0
x^2 -2x - 15 = 0
(x-5)(x+3) = 0
x = 5 or x = -3
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x cannot be negative; so x = 5
Shorter side = x = 5
Longer side = 2x+2 = 12
Hypotenuse = x+8 = 13
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Cheers,
Stan H.