Question

A rectangular exercise mat has a perimeter of 36 feet. The length of the mat is twice the width. Write and solve an equation to determine the length, in feet, of the mat. Then find the area, in square feet, of the mat.

Answer 1

Hello!

The answers are:

- Length

`length=2width=12feet`

- Width

`width=6feet`

- Area

`Area=72feet^(2)`

Why?

We are given the perimeter of a rectangular mat, and we are asked to find the area, and write an equation to determine the length, if feet, of the mat. To solve this problem we need to remember the equation of the perimeter of a rectangle, which is:

`Perimeter=2length+2width`

Using the given information we have,

`36feet=2length+2width`

Also, we know that the length is twice the width, so:

`length=2width`

Then, substituting the second equation into the first equation, we can find the width of the mat.

Substituting, we have:

`36feet=2(2width)+2width`

`36feet=4width+2width`

`36feet=6width`

`[tex](36feet)/(6) =width`\\width=\frac{36feet}{6} =6feet[/tex]

Then, substituting the width into the second equation, we can find the length of the mat,

Substituting, we have:

`length=2width`

`length=2(6feet)=12feet`

Then, finding the area, we have:

`A=length*width=12feet*6feet=72feet^(2)`

Have a nice day!