SOLUTION: The length of the longer leg of a right triangle is 6m more than twice the length of the shorter leg. The length of the hypotenuse is 9m more than twice the length of the shorter

Algebra ->  Pythagorean-theorem -> SOLUTION: The length of the longer leg of a right triangle is 6m more than twice the length of the shorter leg. The length of the hypotenuse is 9m more than twice the length of the shorter      Log On


   

Question 987219: The length of the longer leg of a right triangle is
6m more than twice the length of the shorter leg. The length of the hypotenuse is 9m more than twice the length of the shorter leg. Find the side lengths of the triangle. Thank you
Found 2 solutions by solver91311, stanbon:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


The sides are , , and . Plug these expressions into the Pythagorean Theorem and solve for . Then calculate and .



Note that any negative value for would be absurd; exclude any negative root.

John

My calculator said it, I believe it, that settles it

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The length of the longer leg of a right triangle is
6m more than twice the length of the shorter leg. The length of the hypotenuse is 9m more than twice the length of the shorter leg. Find the side lengths of the triangle. Thank you
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shorter leg: x
longer leg:: 2x+6
hypot:: 2x+9
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Equation:
(2x+9)^2 = x^2 + (2x+6)^2
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4x^2 + 36x + 81 = x^2 + 4x^2 + 24x + 36
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x^2 -12x - 45 = 0
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x = 15
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Ans:
shorter leg = 15
longer leg = 36
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Cheers,
Stan H.
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