SOLUTION: How do I go about solving this problem. The longer leg of a right triangle is 1 meter longer than the shorter leg. The hypotenuse is 1 meter than twice the shorter leg. Find the le

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Question 645258: How do I go about solving this problem. The longer leg of a right triangle is 1 meter longer than the shorter leg. The hypotenuse is 1 meter than twice the shorter leg. Find the lenvth of the shorter leg of the triangle.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
How do I go about solving this problem. The longer leg of a right triangle is 1 meter longer than the shorter leg. The hypotenuse is 1 meter less than twice the shorter leg. Find the lenvth of the shorter leg of the triangle.
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Let the shorter leg be "x".
Longer leg = "x+1"
Hypotenuse = "2x-1"
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Equation:
(2x-1)^2 = (x+1)^2 + x^2
4x^2 - 4x + 1 = x^2 + 2x + 1 + x^2
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4x^2 -4x + 1 = 2x^2 + 2x + 1
2x^2 -6x = 0
2x(x-3) = 0
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Positive solution:
x = 3 (shorter leg)
x+1 = 4 (longer leg)
2x-1 = 5 (hypotenuse)
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Cheers,
Stan H.
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