Solve the problem.
-A gardener is fencing off a rectangular area with a fixed perimeter of $80 \mathrm { ft }$. What is the maximum area?
A) $5 \mathrm { sq } \mathrm { ft }$
B) $1600 \mathrm { sq } \mathrm { ft }$
C) $20 \mathrm { sq } \mathrm { ft }$
D) $400 \mathrm { sq } \mathrm { ft }$

Question

Quizplus · Accepted Answer

The maximum area of a rectangle with a fixed perimeter is achieved when the rectangle is a square. Given a perimeter of 80 ft, each side of the square would be 20 ft (since $P = 4s$, where $P$ is the perimeter and $s$ is the length of one side, thus $s = \frac{P}{4} = \frac{80}{4} = 20$). The area of a square is $s^2$, so the maximum area is $20^2 = 400 \mathrm { sq } \mathrm { ft }$.

Solve the Problem 80ft80 \mathrm { ft }80ft What Is the Maximum Area? A)

Solve the Problem $80 \mathrm { ft }$ What Is the Maximum Area?
A)