Solve the problem.
-A rectangular playground is to be fenced off and divided in two by another fence parallel to one side of the playground. 528 feet of fencing is used. Find the dimensions of the playground that maximize the
Total enclosed area.
A)88 ft by 132 ft
B)132 ft by 132 ft
C)44 ft by 198 ft
D)66 ft by 132 ft

Question

Quizplus · Accepted Answer

The dimensions that maximize the total enclosed area for a given perimeter in a rectangle are those of a square or as close to a square as possible. However, since the playground is divided into two equal parts by a fence parallel to one side, the optimal configuration doubles one dimension. The total fencing used includes the two lengths, the two widths, and the dividing fence. If we let one side be $x$ and the other be $y$, the total fencing used is $2x + 3y = 528$. The configuration that comes closest to a square for each half (considering the dividing fence) is 88 ft by 132 ft, where the longer dimension is effectively halved by the dividing fence, making each section 66 ft by 88 ft, which is the closest to a square configuration possible given the constraint.

Solve the Problem. -A Rectangular Playground Is to Be Fenced Off and Divided