The width of a rectangle is one half its length; the perimeter of the rectangle is 54 cm. What are the width and length of the rectangle?

To find the dimensions of the rectangle, let’s define the length and width based on the information given.

Let the length of the rectangle be represented as L.

According to the problem, the width W is one half of the length, which gives us the equation:

W = rac{1}{2}L

The formula for the perimeter P of a rectangle is:

P = 2L + 2W

We know that the perimeter is 54 cm, so we can write:

54 = 2L + 2W

Now, substitute the expression for W from the first equation into the perimeter equation:

54 = 2L + 2(rac{1}{2}L)

This simplifies to:

54 = 2L + L

Which can be rewritten as:

54 = 3L

Now, divide both sides by 3:

L = 18

Now that we have the length, we can find the width:

W = rac{1}{2}L = rac{1}{2} imes 18 = 9

So, the length of the rectangle is 18 cm and the width is 9 cm.