Question 275267: In a right triangle one side is 1 unit longer than the other side and the perimeter is 12 feet. Find the length of the hypotenuse. Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! In a right triangle one side is 1 unit longer than the other side and the perimeter is 12 feet. Find the length of the hypotenuse.
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shorter side: x
longer side: x+1
hypotenuse: sqrt(x^2 + x^2+2x+1) = sqrt(2x^2 + 2x + 1)
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Equation:
x + x+1 + sqrt(2x^2 + 2x + 1) = 12
sqrt(2x^2 + 2x + 1) = 11-2x
Square both sides:
2x^2 + 2x + 1 = 121 - 44x + 4x^2
2x^2 -46x + 120 = 0
x^2 - 23x + 60 = 0
(x-20)(x-3) = 0
x = 3
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If x = 3:
hypotenuse = sqrt(18+6 + 1) = 5
short side = 3
longer side = 4
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Cheers,
Stan H.
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