A gardener is fencing off a rectangular area with a fixed perimeter of $72 \mathrm{ft}$. What is the maximum area?
A) $18 \mathrm{ft}^{2}$
B) $1296 \mathrm{ft}^{2}$
C) $4.5 \mathrm{ft}^{2}$
D) $324 \mathrm{ft}^{2}$

Question

Quizplus · Accepted Answer

The maximum area for a given perimeter in a rectangle is achieved when the rectangle is a square. The perimeter of a square is $4s$, where $s$ is the side length. Given a perimeter of $72 \mathrm{ft}$, each side of the square is $72 \mathrm{ft} / 4 = 18 \mathrm{ft}$. The area of a square is $s^2$, so the maximum area is $18^2 = 324 \mathrm{ft}^{2}$.

A Gardener Is Fencing Off a Rectangular Area with a Fixed