Question

the length of a rectangle is two more than the width. if the perimeter is 28, find the length and the width of the rectangle, let w represent the width and l represent the length.

Answer 1

You have that the perimeter of a rectangle is 28. In order to find the values of length and width of the rectangle, you take into account the following formula for the perimeter of a rectangle:

`P=2w+2l`

where w is the width and l is the length. You have that the length l is twice the width w of the rectangle, that is l=2w. By replacing this expression for l into theformula for the calculation of the perimeter you obtain:

`P=2w+2(2w)=2w+4w=6w`

Thus, you have that P = 6w. You solve this equation for w, and also replace the value of P, just as follow:

`\begin{gathered} P=6w \\ w=(P)/(6)=(28)/(6)=(14)/(3)=4.66 \end{gathered}`

Then, the width is 4.66. The length is:

`l=2w=2(4.66)=9.33`

length = 9.33