Your solution is \(\displaystyle P = \frac{A^2}{3}\\)
Let's substitute our solution into the equation to check:
\(\displaystyle A = \sqrt{3 \frac{A^2}{3}\ }\ = \sqrt{A^2}\\)
This is only true for non-negative A.
So, let's revise the solution:
\(\displaystyle P = \frac{A^2}{3}\\), for non-negative A.