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

Answer:

The width is 9 cm and the length is 16 cm

Step-by-step 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

Answer 2

Answer:

$Length=16\ cm\\\\Width=9\ cm$

Step-by-step 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:

$Length=16\ cm\\\\Width=9\ cm$