Real world applications of quadratic’s

Question

You have a 500-foot roll of chain link fencing and a large field. You want to fence and a rectangular playground area. What are the dimensions of the largest such a playground area you can enclose? What is the area of the playground?

Answer 1

For a given perimeter the geometric figure with the greatest area is the circle. Yet here you want a rectangle.Therefore the figure is a square.

In this case the square is 125 x 125

What is the area?