A wire 60 cm long is to be cut into two pieces. One of the pieces will be bent into the shape of a square and the other into the shape of an equilateral triangle.

Question

The wire is to be cut in order that the sum of the areas of the square and the triangle is to be a maximum. An equation that can be used to model the sum of the areas is A(x)= (x^2/16)+)sqrt3(60-x)^2/18) . Determine the boundaries and the corresponding areas. You need not solve further.

Answer 1

x is the length of one wire.

take the derivative of A

A'=0=2x/8 + 1/2 (2*3(60-x)(-1)/18sqrt3(60-x)^2/18)
check the derivative, I am uncertain what you meant for the second part.

solve for x.