# The length of a rectangle is 7 feet larger than the width. The perimeter of the rectangle is 26 ft. How do you write an equation to represent the perimeter in terms of its width (w). What is the length?

Nov 4, 2016

An equation to represent the perimeter in terms of its width is: $p = 4 w + 14$ and the length of the rectangle is $10$ ft.

#### Explanation:

Let the width of the rectangle be $w$.

Let the length of the rectangle be $l$.

If the length ($l$) is 7 feet longer than the width, then the length can be written in terms of the width as:

$l = w + 7$

The formula for perimeter of a rectangle is:

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

Substituting $w + 7$ for $l$ gives an equation to represent the perimeter in terms of its width:

$p = 2 \left(w + 7\right) + 2 w$

$p = 2 w + 14 + 2 w$

$p = 4 w + 14$

Substituting $26$ for $p$ allows us to solve for $w$.

$26 = 4 w + 14$

$26 - 14 = 4 w + 14 - 14$

$12 = 4 w$

$\frac{12}{4} = 4 \frac{w}{4}$

$w = 3$

Sustituting $3$ for $w$ in the equation above, $l = w + 7$ allows us to determine the length:

$l = 3 + 7$

$l = 10$