Question

The perimeter of a rectangle is 24 inches, how do you find the dimensions if its length is 3 times greater than its width?

Answer 1

Length: 9 inches
Width: 3 inches

Explanation:

You use the information given to you to write a system of two equations.

The perimeter of a rectangle is equal to the sum of its length and its width, multiplied by `2`

`color(blue)(P = 2 * (L + w))`

In your case, you know that

`2(L+w) = 24`

This will be your first equation.

Now focus on the fact that its length is 3 times greater than its width. This can be written like this

`L = 3 * w`

Your system will be

`{( 2(L+w) = 24), (L = 3w) :}`

To solve for the length and width of the rectangle, use the expression you have for `L` in the first equation to get `w`

`2 * ( 3w + w) = 24`

`2 * 4w = 24 => w = 24/8 = color(green)(3)`

This means that `L` is equal to

`L = 3 * 3 = color(green)(9)`