A rectangular playground is to be fenced off and divided in two by another fence parallel to one side of the playground. Five hundred and forty feet of fencing is used. Find the dimensions of the playground that maximize the total enclosed area. What is the maximum​ area?

Answer 1

the fence must be divided equally among the two lengths and three widths. So, 540/2 = 270, so the playground is largest if it is

135x90

You can verify this by finding the vertex of the parabola

y = x(540-2x)/3