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Let's have a right angle triangle. The sides have lengths equal to rational numbers. The area of the triangle is equal to 39, the length of the hypotenuse is 31.3 and the difference of the other two sides is 28.7. What are the lengths of these two sides?

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    $\begingroup$ Why is this a puzzle? It's the solution of two simultaneous equations, which give a quadratic equation to solve, and has a redundant piece of information. It's straight forward math. $\endgroup$ Mar 26, 2023 at 21:24
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    $\begingroup$ even chatgpt can solve this :) $\endgroup$
    – Oray
    Mar 26, 2023 at 21:43
  • $\begingroup$ In addition to being soluble with any two of the three numerical values, we can also solve without knowing that the lengths are rational. I’m unable to discern an especially elegant way of using the information. $\endgroup$
    – Daniel S
    Mar 26, 2023 at 22:31

1 Answer 1

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This is a simple algebra exercise. Combining $b - a = 28.7$ with $a \cdot b = 2 \cdot 39$ gives $a^2 + 28.7 a - 78 = 0$. Solving this quadratic gives $a=2.5$, $b=31.2$ as the only possible answer, and you can use the hypotenuse information to double check that this is the correct solution. Not really much of a puzzle, more of a homework problem.

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