Question

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?

Answer 1

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 = 4w - 7`

The formula for the perimeter of a rectangle is:

`p = 2*l + 2*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*(4w-7) + 2w`

`56 = 8w - 14 + 2w`

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

`70 = 8w - 0 + 2w`

`70 = 10w`

`70/10 = (10w)/10`

`7 = w`

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

`l = 4*7 - 7`

`l = 28 - 7`

`l =21`