SOLUTION: Find the length of the shorter leg of a right triangle if the longer leg is 12 feet more than the shorter leg and the hypotenuse is 12 feet less than twice the shorter leg.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: Find the length of the shorter leg of a right triangle if the longer leg is 12 feet more than the shorter leg and the hypotenuse is 12 feet less than twice the shorter leg.       Log On


   

Question 673245: Find the length of the shorter leg of a right triangle if the longer leg is 12 feet more than the shorter leg and the hypotenuse is 12 feet less than twice the shorter leg.

Found 2 solutions by solver91311, stanbon:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Let represent the measure of the short leg. Then is the measure of the long leg, and is the measure of the hypotenuse. Use Pythagoras:



Solve for the non-zero root.

John

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Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Find the length of the shorter leg of a right triangle if the longer leg is 12 feet more than the shorter leg and the hypotenuse is 12 feet less than twice the shorter leg.
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Let the shorter leg be "x".
Other leg: "x+12"
Hypotenuse: "2x-12"
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Equation:
(2x-12)^2 = x^2 + (x+12)^2
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4x^2 - 48x + 144 = 2x^2 + 24x + 144
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2x^2 - 72x = 0
2x(x-36) = 0
Positive solution:
x = 36 (shorter leg)
x+12 = 48 (longer leg)
2x-12 = 60 (hypotenuse)
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Cheers,
Stan H.