Question

The length of a rectangle is 3 cm more than four times the width. If the perimeter of the rectangle is 36 cm, what are its dimemions?

Answer 1

length`=10.5` `cm`
width`=7.5` `cm`

Explanation:

Start by making let statements to represent variables as the length and width as stated in the question.

Let `4x` represent the width.
Let `4x+3` represent the length.

`2[(4x)+(4x+3)]=36`
`2[8x+3]=36`
`8x+3=18`
`8x=15`
`x=15/8`

To find the dimensions, substitute `x=15/8` into `4x` (width) and `4x+3` (length).

Finding the width

`w=4x`

`w=4(15/8)`

`w=color(red)cancelcolor(black)4(15/color(red)cancelcolor(black)8^2)`

`w=15/2`

`w=7.5`

Finding the length

`l=4x+3`

`l=4(15/8)+3`

`l=color(red)cancelcolor(black)4(15/color(red)cancelcolor(black)8^2)+3`

`l=15/2+3`

`l=21/2`

`l=10.5`

`:.`, the length is `10.5` `cm` and the width is `7.5` `cm`.