Question

The length of a rectangle is 3 times the width. The perimeter is 48 centimeters. What is the area?

Answer 1

`108cm^2`

Explanation:

So, the perimeter of any rectangle is given by adding the length twice and the width twice:

`P = L +W+L+W`

In our particular case the length is 3 times the width:

`L = 3 xx W`

Substituting that, and the 48 centimeters we know the perimeter to be into the first equation, we get:

`48=3 xx W+W+3 xx W+W`
`48=8 xx W`
`W==48/8`
`W=6`

So, if the width is 6, the length is:

`L = 3 xx W = 3 xx 6 = 18`

Now, the area of any rectangle is given by multiplying the length and the width:

`A=L xx W`

In our case `L = 18` and `W = 6`, so:

`A = 18 xx 6 = 108`

Also, remember to "multiply" the units. In this case centimeter times centimeter gives us centimete`r^2` or `cm^2`

So the area is `108cm^2`