A rectangle has sides of integer length (when measured in $\mathrm{cm}$ ) and an area of $36 \mathrm{~cm}^{2}$. What is the maximum possible perimeter of the rectangle?
(A) $72 \mathrm{~cm}$
(B) $80 \mathrm{~cm}$
(C) $26 \mathrm{~cm}$
(D) $74 \mathrm{~cm}$
(E) $48 \mathrm{~cm}$
A rectangle has sides of integer length (when measured in $\mathrm{cm}$ ) and an area of $36 \mathrm{~cm}^{2}$. What is the maximum possible perimeter of the rectangle?
(A) $72 \mathrm{~cm}$
(B) $80 \mathrm{~cm}$
(C) $26 \mathrm{~cm}$
(D) $74 \mathrm{~cm}$
(E) $48 \mathrm{~cm}$

## Solution

Since the area is $36 \mathrm{~cm}^{2}$ and the sides have integer length, then we make a table of the possibilities:

Side lengths

1,36

2, 18

3,12

4,9

6,6
Perimeter

$$
\begin{aligned}
2(1+36) & =74 \\
2(2+18) & =40 \\
2(3+12) & =30 \\
2(4+9) & =26 \\
2(6+6) & =24
\end{aligned}
$$

So the maximum possible perimeter is $74 \mathrm{~cm}$.