SOLUTION: A right triangle has sides whose lengths in feet are consecutive even integers. determine the length of each side?

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Question 203722This question is from textbook Algeba Struture and Method
: A right triangle has sides whose lengths in feet are consecutive even integers. determine the length of each side? This question is from textbook Algeba Struture and Method

Answer by nerdybill(7384) About Me  (Show Source):
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A right triangle has sides whose lengths in feet are consecutive even integers. determine the length of each side?
.
Let x = shortest side
then
x+2 = second side
x+4 = hypotenuse
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Applying Pythagorean theorem:
x^2 + (x+2)^2 = (x+4)^2
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}
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Throwing out the negative solution we have:
x = 6
x+2 = 8
x+4 = 10
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The three sides are 6, 8, 10