The length of a rectangle is 6 more than twice its width. If the perimeter of the rectangle is 120 , what is its width?
(A) 8
(B) 18
(C) 27
(D) 38
(E) 22
Solution 1

Since the perimeter of a rectangle equals twice the length plus twice the width, then the length plus the width equals $120 \div 2=60$.

Since the length equals twice the width plus 6 , then twice the width plus the width equals $60-6=54$.

In other words, three times the width equals 54 , so the width equals $54 \div 3=18$.

## Solution 2

Let the width of the rectangle be $w$.

Then the length of the rectangle is $2 w+6$.

Since the perimeter is 120 , then

$$
\begin{aligned}
2 w+2(2 w+6) & =120 \\
2 w+4 w+12 & =120 \\
6 w & =108 \\
w & =18
\end{aligned}
$$

so the width is 18 .

ANSWER: (B)