Question

Find the lenght of the sides of an isosceles triangle with a given perimeter if its area is to be as great as possible.

let k be the the length of the two iso sides, so the other side is P-2k. Call that the base.

Using Heron's formula:
Area=SQRT(s(s-a)(s-b)(s-c)),

but s= P/2 , a and b are equal, and c is P-2a

area= sqrt(s(s-a)^2 (s-P+2a))

dA/d=0= you do it. Solve for a