#### Answer

The width of the rectangle is 36 centimeters.

#### Work Step by Step

Let w represent the width of the rectangle.
The ratio of the width to its length is $\frac{4}{5}$, and the length is 45 centimeters.
We set up the following proportion:
$\frac{4}{5}$ = $\frac{w}{45}$
We cross multiply to obtain:
4 $\times$ 45 = 5 $\times$ w
180 = 5w
Divide both sides by 5.
w = 36.
The width of the rectangle is 36 centimeters.