there are so many ways to solve this problem. i'll give you two of them. i'll assume that are the length of the sides and where is fixed.

Solution 1: by Heron's formula: so we only need to maximize the function

so we must solve theis system: which will easy give you and thus so the equilateral

triangle with the side of length is the answer.

Solution 2: following our notation in solution 1, by AM-GM inequality we have: which gives us: