Question 387378: the perimiter of a right triangle is 12. the lengths of the legs of the triangle are 3 and x. the length of the hypotenuse is y.
how can i set up a system of equation that could be used to find the hypotenuse and the other of the right triangle?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! the perimeter of a right triangle is 12.
the lengths of the legs of the triangle are 3 and x.
the length of the hypotenuse is y.
how can i set up a system of equation that could be used to find the hypotenuse and the other of the right triangle?
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Express the hypotenuse in terms of "x" using Pythagoras.
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y^2 = 3^2 + x^2
y = sqrt(9+x^2)
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Then the perimeter is 3 + x + sqrt(9+x^2) = 12
Solve for "x":
x + sqrt(9+x^2) = 9
sqrt(9+x^2) = 9-x
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Square both sides to get:
9+x^2 = 81-18x+x^2
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9 = 81-18x
18x = 72
x = 4
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The sides are 3,4,y
y = sqrt(9+x^2) = sqrt(9+16) = 5
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Cheers,
Stan H.
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