A wire 60 cm long is to be cut into 2 pieces. One of the pieces will be bent into the shape of a square and the other into an equilateral triangle. 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 total area of the shapes is:
a(x) = x^2 / 16 + sqrt(3(60 - x)^2 / 18
Determine the boundaries and the corresponding areas.
x equals the perimeter of the square
x - 60 equals the perimeter of the rectangle