# The plans for a shed call for a rectangular floor with a perimeter of 198 ft. The length is The two times the width. How do you find the length and width?

Jan 7, 2017

See full explanation for how to find the length and width below in the explanation:

#### Explanation:

The formula for a perimeter is:

$p = 2 w + 2 l$

Where
$p$ is the perimeter
$w$ is the width
$l$ is the length.

And, we know from the problem:

$l = 2 w$

We can then substitute $2 w$ for $l$ in the equation for the perimeter to give:

$p = 2 w + \left(2 \times 2 w\right)$

$p = 2 w + 4 w$

$p = 6 w$

We also know the perimeter will be 198 ft so we can substitute this for $p$ and solve for $w$, the width:

$198 = 6 w$

$\frac{198}{\textcolor{red}{6}} = \frac{6 w}{\textcolor{red}{6}}$

$33 = w$ or $w = 33$

And because we know:

$l = 2 w$ we can substitute $33$ for $w$ and solve for $l$:

$l = 2 \times 33$

$l = 66$

The length of the floor will be 66 ft and the width will be 33 ft.