# The perimeter of a standard-sized rectangular rug is 28 ft. The length is 2 ft longer than the width. How do you find the dimensions. What is the width?

Nov 28, 2016

The dimensions are 6 feet by 8 feet and the width is 6 feet.

#### Explanation:

The formula for the perimeter of a rectangle is:

$p = 2 \cdot w + 2 l$ where $p$ is the perimeter, $w$ is the width and $l$ is the length.

We are told the length is 2 ft longer than the width. So, we can write this as:

$l = w + 2$

We are also given the perimeter or $p$.

So substituting $28$ for $p$ and $w + 2$ for $l$ we can rewrite this formula as follows and solve for $w$ while keeping the equation balanced:

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

$28 = 2 w + 2 w + 4$

$28 = 4 w + 4$

$28 - 4 = 4 w + 4 - 4$

$24 = 4 w$

$\frac{24}{4} = \frac{4 w}{4}$

$w = 6$

We can number substitute $6 W f \mathmr{and}$w$\in t h e e q u a t i o n f \mathmr{and}$l# to determine the length:

$l = 6 + 2$

$l = 8$