SOLUTION: If the sum of the two sides of a right triangle is 49 inches and the hypotenuse is 41 inches, find the other two sides.

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Question 1000589: If the sum of the two sides of a right triangle is 49 inches and the hypotenuse is 41 inches, find the other two sides.
Found 2 solutions by josgarithmetic, Alan3354:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
x and 49-x are the legs.

x%5E2%2B%2849-x%29%5E2=41%5E2-----Pythagorean Theorem Formula applied.

x%5E2%2B49%5E2-98x%2Bx%5E2=41%5E2
2x%5E2-98x%2B49%5E2-41%5E2=0
2x%5E2-98x%2B%2849%2B41%29%2849-41%29=0------seeing difference of two squares
2x%5E2-98x%2B90%2A8=0
x%5E2-49x%2B45%2A8=0-----might be factorable, but too many possibilities to try.
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discriminant? 49%5E2-4%2A1%2A45%2A8=2401-45%2A8=2041
2041=13%2A157, so not a square.

x=%2849%2B-+sqrt%282041%29%29%2F2
Other leg then 49-%2849%2B-+sqrt%282041%29%29%2F2.

The PLUS form will not work (as would be found if continuing this way).
Try the MINUS form.

highlight%28x=%2849-sqrt%282041%29%29%2F2%29 and then other leg is highlight%2849-%2849-sqrt%282041%29%29%2F2%29. You should find that these give reasonable values.


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Be aware of the site page, http://www.mathwarehouse.com/arithmetic/numbers/prime-number/prime-factorization-calculator.php

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
x and 49-x are the legs.
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x%5E2+%2B+%2849-x%29%5E2+=+41%5E2+=+1681
2x%5E2+-+98x+%2B+2401+=+1681
2x%5E2+-+98x+%2B+720+=+0
x%5E2+-+49x+%2B+360+=+0
(x-9)*(x-40) = 0
Sides are 9 & 40
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