Question

3. 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. Find the length of the shorter leg.
is 10 more than the​

Answer 1

Answer:

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

hope it helps