Question

The length of a rectangular mailing label is 2 centimeters less than twice the width. The perimeter is 50 centimeters. Find the dimensions of the label.

Answer 1

`Length=16\ cm\\\\Width=9\ cm`

Explanation:

We know that the lenght (
`l`) of the rectangular mailing label is 2 centimeters less than twice the width (
`w`). This is:

`l=2w-2`

The formula for calculate the perimeter of a rectangle is:

`P=2l+2w`

Then, we must substitute the perimeter and
`l=2w-2` into the formula
`P=2l+2w` and solve for "w":

`50=2(2w-2)+2w\\\\50=4w-4+2w\\\\54=6w\\\\w=9`

Now substitute the value of "w" into
`l=2w-2` to find the lenght. Then:

`l=2(9)-2=16`

Therefore, the dimensions are:

`Length=16\ cm\\\\Width=9\ cm`

Answer 2

The width is 9 cm and the length is 16 cm

Explanation:

Let the width be x centimeters.

If the length of a rectangular mailing label is 2 centimeters less than twice the width, then the length is 2x-2 centimeters.

The perimeter is the sum of all sides, so

`x+(2x-2)+x+(2x-2)=50\\ \\x+2x-2+x+2x-2=50\\ \\6x-4=50\\ \\6x=54\\ \\x=9\\ \\2x-2=2\cdot 9-2=18-2=16`

The width is 9 cm and the length is 16 cm