# The length of a rectangle is twice the width. The perimeter of the rectangle can be expressed as 3* 13.7 What is the width?

Nov 19, 2016

The width is 6.85.

#### Explanation:

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

For this problem we are told the "length is twice the width" or $l = 2 w$. Therefore we can substitute $2 w$ for $l$ in the equation for the perimeter giving:

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

For this problem we are also told the perimeter is $3 \cdot 13.7$ which is $41.1$ so we can substitute $41.1$ for $p$ in the equation and solve for $w$:

$41.1 = 2 \cdot \left(2 w\right) + 2 w$

$41.1 = 4 w + 2 W$

$41.1 = 6 w$

$\frac{41.1}{6} = \frac{6 w}{6}$

$6.85 = 1 w$

$w = 6.85$