Question

The length of a rectangle is five inches less than three times its width. If the perimeter

of the rectangle is 150 inches, find the dimensions.

L=40 in. ; W=35 in.
L=60 in. ; W=45 in.
L=50 in. ; W=25 in.
L=55 in. ; W=20 in.

Answer 1

L = 55 in, W = 20 in

Explanation:

Hi there!

First we have to set up an equation for the length, which can be written as 3x - 5.

The formula for perimeter of a rectangle is 2l + 2w = p, so we can plug in some values here.

l = 3x - 5

w = x

`2(3x-5) + 2(x) = 150`

Now we just have to solve!

`6x - 10 + 2x = 150`

When we combine like terms and add ten to both sides, we are left with

`8x = 160`, which means x = 20

Using this, that means the width is 20

We can find the perimeter by plugging 20 in for x.
`l = 3(20) -5`

This means the length is 55.