Question

The length of a rectangle is 2 m more than twice its width. Find the length and width of the rectangle, if its perimeter is 28 m.

Please use algebra.

Answer 1

Length is 10

Width is 8

Explanation:

The formula for the perimeter of a rectangle is:

`P=2l+2w`

We are told that the length l is 2 more than twice the width w. In other words:

`l=2+2w`

Also, we are given that the perimeter is 28. Therefore:

`P=2l+2w\\28=2(2+2w)+2w`

Distribute:

`28=4+4w+2w`

Combine like terms:

`28=4+6w`

Subtract 4 from both sides:

`6w=24`

Divide by 6:

`w=4`

So, the width is 4.

And the length is 2 more than twice the width. Thus:

`l=2+2(4)\\l=2+8=10`

The length is 10.

And we are done :)