Find the dimensions of the playground that maximize the total enclosed area. What is the maximum​ area?

Question

A rectangular playground is to be fenced off and divided in two by another fence parallel to one side of the playground. Seven hundredSeven hundred and eightyand eighty feet of fencing is used.

Answer 1

If the entire playground is L feet long and W feet wide, the perimeter would be 2(L+W) = 780 if not for the bisecting fence. Since we want to use a little of the total fencing to bisect the area as possible, we would put the bisecting potion parallel to the width, thus 780 = 2(L+W) + W = 2L + 3W Since the area of a rectangle stays constant no matter how you change the lengths of the sides, that means we can assume it also holds true for a square. Thus, L = W and that makes our equation

780 = 2L + 3W = 2L + 3L = 5L

L = 780/5 = 156 for a square and the area would be L*L = 156² = 24,336 square feet