Solve the problem. Use 3.14 for $\pi$. Round your answer to the nearest hundredth.
-Robert has a rectangular garden that is currently $400 \mathrm { ft } ^ { 2 }$ and has a perimeter of $80 \mathrm { ft }$. He wants to increase the size of his garden by $4 \mathrm { ft }$ in both directions. What will be the area of his expanded garden?
A) $96 \mathrm { ft } ^ { 2 }$
B) $1600 \mathrm { ft } ^ { 2 }$
C) $576 \mathrm { ft } ^ { 2 }$
D) $160 \mathrm { ft } ^ { 2 }$

Question

Quizplus · Accepted Answer

The original dimensions of the garden can be found by setting up equations based on the given area and perimeter. Let the length be $l$ and the width be $w$. The area is $lw = 400$ and the perimeter is $2l + 2w = 80$. Solving these equations, we find $l = 20$ and $w = 20$. Increasing each dimension by 4 feet results in new dimensions of $24 \times 24$, giving an area of $576 \mathrm { ft } ^ { 2 }$.

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