Hi everyone, im trying to do a question involving Heron's Formula where,

and s = (a + b + c)/2

Using Lagrange Multipliers, i'm trying to find in terms of the ﬁxed perimeter P = 2s, the maximum area of aright-angled triangle with perimeter P.

There's a pretty standard proof out there for Heron's formula to maximise an equilateral triangle, so im trying to adapt it for a right angled triangle by labelling the sides "h", "hsin(t)" and "hcos(t)" where one of the interior angles of the triangle is "t". Is this even the right way to go? I get pretty stuck at this point anyway, trying to produce gradients, and the consequencial Lagrange Multipliers.

Anyone able to get me stated on this?

Thanks