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I was sure that this has been asked before, but the title did not match.

So if the area of a right triangle is A and the perimeter is P, express the sides a and b in terms of A and P.

marty cohen
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    You know how to write down equations involving $a,b,A,P$, correct? How far do you get when you do that? – KReiser Dec 29 '19 at 04:36
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    To be clear, marty, is this intended to be a canonical question where you will post a detailed explanation as an answer later on? If so that could excuse the current form of the question, but as it stands I'm sure you're aware that it seems to be rather lacking in context. – YiFan Tey Dec 29 '19 at 04:38
  • Well, at least it was answered (the same way I did) before it was closed. – marty cohen Dec 29 '19 at 05:19

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$a+b+\sqrt{a^2+b^2}=a+b+\sqrt{(a+b)^2-4A}=P, {a}{b}=2A$

This leads to $P^2-2P(a+b)=-4A$, hence $a+b=\frac{P^2+4A}{2P}$

So $a$ and $b$ are roots of the quadratic equation $x^2-\frac{P^2+4A}{2P}x+2A=0$

Huang
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