# The length of a rectangle is 7 yards less than 4 times the width, the perimeter is 56 yards, how do you find the length and the width of the rectangle?

Dec 9, 2016

The width is 7 yards and the length is 21 yards.

#### Explanation:

First, let's define our variables.

Let $l$ = the length of the rectangle.
Let $w$ = the width of the rectangle.

From the information provided we know the relationship between the length and the width:

$l = 4 w - 7$

The formula for the perimeter of a rectangle is:

$p = 2 \cdot l + 2 \cdot w$

We know the perimeter of the rectangle and we know the length in terms of the width so we can substitute these values into the formula and solve for the width:

$56 = 2 \cdot \left(4 w - 7\right) + 2 w$

$56 = 8 w - 14 + 2 w$

$56 + 14 = 8 w - 14 + 14 + 2 w$

$70 = 8 w - 0 + 2 w$

$70 = 10 w$

$\frac{70}{10} = \frac{10 w}{10}$

$7 = w$

Now that we know the width is $7$ we can substitute this into the formula for the length:

$l = 4 \cdot 7 - 7$

$l = 28 - 7$

$l = 21$