#### Answer

The width of the rectangle is $5.5$ cm, and the length is $16.5$ cm.

#### Work Step by Step

Let's set up an equation to find the length of the rectangle using the information we are given:
$l = 3w$, where $l$ is the length and $w$ is the width.
We can also set up an equation for the perimeter:
$2l + 2w = 44$
We see that in the first equation, we already have $y$ expressed in terms of $x$, so we substitute this expression for $y$ in the second equation to find $x$:
$2(3w) + 2w = 44$
Multiply first:
$6w + 2w = 44$
Combine like terms:
$8w = 44$
Divide each side by $8$ to solve for $w$:
$w = 5.5$ cm
Now, plug in the value for $w$ into the first equation to find $l$:
$l = 3(5.5)$
Multiply to solve for $l$:
$l = 16.5$ cm