a triangular field is to be enclosed by p feet of fencing so as to maximize the area of the field. find the lengths of sides of this triangle. [Hint: Heron's formula for the area of a triangle with side lengths x, y, and z is A= square root of (s(s-x)(s-y)(s-z)), where s= 1/2 (x+y+z) is the semiperimeter.]
so, there's a function with two constraints.
i took the gradient of each.
i set gradient p = lambda gradientA + mu gradientS
this is extremely complicated though and i don't know how to solve it.
the back of the book says x=y=z=p/3
any suggestions? thank you so much