Question

Please solve with explanation (high points)

Answer 1

So, we know that:

`A=(1)/(2)ab\\P=a+b+c\\a^2+b^2=c^2`

We also know that
`(a+b)^2=a^2+2ab+b^2`. We will use that fact to find
`c` in terms of
`A` and
`P`.

`A=(1)/(2)ab\Rightarrow 2ab=4A\\P=a+b+c\Rightarrow a+b=P-c`

Therefore:

`(P-c)^2=c^2+4A\\P^2-2cP+c^2=c^2+4a\\2cP=P^2-4A\\c=(P^2-4A)/(2P)`