# The length of a rectangle is one more than four times its width. if the perimeter of the rectangle is 62 meters, how do you find the dimensions of the rectangle?

Jan 8, 2017

See full process for how to solve this problem below in the Explanation:

#### Explanation:

First, let's define the length of the rectangle as $l$ and the width of the rectangle as $w$.

Next, we can write the relationship between the length and width as:

$l = 4 w + 1$

We also know the formula for the perimeter of a rectangle is:
$p = 2 l + 2 w$

Where:

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

We can now substitute $\textcolor{red}{4 w + 1}$ for $l$ in this equation and 62 for $p$ and solve for $w$:

$62 = 2 \left(\textcolor{red}{4 w + 1}\right) + 2 w$

$62 = 8 w + 2 + 2 w$

$62 = 8 w + 2 w + 2$

$62 = 10 w + 2$

$62 - \textcolor{red}{2} = 10 w + 2 - \textcolor{red}{2}$

$60 = 10 w + 0$

$60 = 10 w$

$\frac{60}{\textcolor{red}{10}} = \frac{10 w}{\textcolor{red}{10}}$

$6 = \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{10}}} w}{\cancel{\textcolor{red}{10}}}$

$6 =$ or $w = 6$

We can now substitute $w$ into our formula for the relationship between $l$ and $w$ and calculate $l$:

$l = \left(4 \times 6\right) + 1$

$l = 24 + 1$

$l = 25$

The length of the rectangle is 25 meters and the width of the rectangle is 6 meters.