# A rectangular Persian carpet has a perimeter of 252 inches. The length of the carpet is 28 in, more than the width. What are the dimensions of the carpet?

Nov 5, 2016

The length of the carpet is 77 inches and the width is 49 inches.

#### Explanation:

The formula for perimeter is $p = 2 l + 2 w$ where $p$ is the perimeter, $l$ is the length and $w$ is the width.

If the length of the carpet is 28 in. more than the width we know:

$l = w + 28$

Substituting $w + 28$ for $l$ and 252 for $p$ in the formula for perimeter and solving for $w$ while keeping the equation balanced gives:

$252 = 2 \left(w + 28\right) + 2 w$

$252 = 2 w + 56 + 2 w$

$252 = 4 w + 56$

$252 - 56 = 4 w + 56 - 56$

$196 = 4 w$

$\frac{196}{4} = \frac{4 w}{4}$

$w = 49$

And substituting $49$ for $w$ in the equation for $l$ gives:

$l = 49 + 28$

$l = 77$