SOLUTION: The longer leg of a right triangle is ten less than three times the shorter leg. The hypotenuse is 4 more than the shorter leg. Please find the length of the shorter leg.

Question 707306: The longer leg of a right triangle is ten less than three times the shorter leg. The hypotenuse is 4 more than the shorter leg. Please find the length of the shorter leg.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The longer leg of a right triangle is ten less than three times the shorter leg. The hypotenuse is 4 more than the shorter leg. Please find the length of the shorter leg.
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L = 3S - 10
H = S + 4
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Equation:
H^2 = S^2 + L^2
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(S+4)^2 = S^2 + (3S-10)^2
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S^2 + 8S + 16 = S^2 + 9S^2 -60S + 100
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8S + 16 = 8S^2 -60S + 100
8S^2 -68S + 84 = 0
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2S^2 - 17S + 21 = 0
(2S-3)(S-7) = 0
S = 3/2 or S = 7
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Feasible answer: Shortest leg = 7
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Cheers,
Stan H.
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