Question

The length of a rectangle is 6 inches longer than it’s width. The perimeter of the rectangle is 36 inches long. How long and how wide is the rectangle.

Answer 1

Length of rectangle = 12 inches

Width of rectangle = 6 inches

Explanation:

Let the width of rectangle in inches be =
`w`

Given: The length of rectangle is 6 inches longer than its width.

So, length of rectangle in inches
`l=w+6`

Perimeter of a rectangle is =
`2(l+w)`

Plugging in
`l=w+6` in the perimeter formula.

Perimeter of rectangle in terms of width =
`2(w+6+w)`

Simplifying and using distribution.

⇒
`2(2w+6)`

⇒
`(2* 2w)+(2*6)`

⇒
`4w+12`

We are given perimeter of rectangle = 36 inches.

So, we can equate to find
`w`

`4w+12=36`

Subtracting both sides by 12.

`4w+12-12=36-12`

`4w=24`

Dividing both sides by 4.

`(4w)/(4)=(24)/(4)`

`w=6` inches

Using
`w=6` to find
`l`

`l=6+6=12` inches

Length of rectangle = 12 inches

Width of rectangle = 6 inches