SOLUTION: You have a right triangle with hypotenuse 25. One of the legs gets decreased by 8 and other gets increased 4 and we still have a right triangle with hypotenuse 25. What are the len

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Question 1058022: You have a right triangle with hypotenuse 25. One of the legs gets decreased by 8 and other gets increased 4 and we still have a right triangle with hypotenuse 25. What are the lengths of the legs in the new triangle? (If you could tell me how you got your answer that would be helpful.)
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
x and y, original dimensions for the right triangle initially.

x%5E2%2By%5E2=25%5E2



The new triangle, also right triangle, same hypotenuse length.
Unclear what kind of increases are described. Assuming addition.

%28x-8%29%5E2%2B%28y%2B4%29%5E2=25%5E2
x%5E2-16x%2B64%2By%5E2%2B8y%2B16=25%5E2
x%5E2%2By%5E2%2B8y-16x%2B64%2B16=25%5E2
25%5E2%2B8y-16x%2B80=25%5E2
8y-16x%2B80=0
y-2x%2B10=0

You might use this last resulting equation and the original triangle equation for this system: system%28x%5E2%2By%5E2=25%5E2%2Cy-2x%2B10=0%29, and you should be able to solve this nonlinear system with no trouble. Try taking y=2x-10, and substitute this in the other equation.

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
(24, 7, 25) and (20, 15, 25).