Eighty metres of fencing are available to enclose a rectangular play area. Determine the dimensions that will enclosed the maximum area. What is the maximum area?

1 answer

2(x+y)=80, so y = 40-x

area = xy = x(40-x) = 40x-x^2

That's just a parabola. Find the vertex and you will have the maximum area.

A little investigation that the rectangular shape of maximum area for a given perimeter is always a square.