Optimization: maximize a triangle surface

See if anyone can help me with this: Among all triangles of perimeter equal to P, find the one with the largest area. (Hint: use the formula $\displaystyle A=\sqrt[ ]{p(p-x)(p-y)(p-z)}$ where $\displaystyle P=2p$, $\displaystyle P$ is the perimeter).

So, I have $\displaystyle f|_s $, I think that must be solved using Lagrange multipliers, at least I don't see any other way.

I've proceeded this way: $\displaystyle f=\sqrt[ ]{p(p-x)(p-y)(p-z)}$, $\displaystyle s=p=\displaystyle\frac{x+y+z}{2}$

Well, I have done so, but all derivatives did wrong (I did $\displaystyle A^2$ arising as if $\displaystyle f=A^2$ and then apply the multiplier to with the 4 conditions ), it became ugly, maybe it was because of that. Anyway, would you tell me if what I did until here is ok? Greetings.