Question

What are the dimensions of a rectangle which has a perimeter of `48 cm`, if its length is `12 cm` longer than twice its width?

Answer 1

Width: `4cm`

Length: `20cm`

Explanation:

Recall that the perimeter of a rectangle is twice the sum of its length and width

So we have

`P=2l+2w`

We are also given that the length of the rectangle in question is 12cm longer than twice it width

Then

`l=12+2w`

Then we can plug in

`P=2w+2l=2w+2(12+2w)`

And simplify

`P=2w+24+4w=24+6w`

Since we know that the perimeter is 48 cm we can say

`P=48=24+6w`

`<=>` subtract 24 from both sides

`24=6w`

`<=>` divide both sides by 6

`4=w`

Then we can plug that in to find l

`l=12+2w=12+2(4)=12+8=20`

Answer 2

Width = `4 cm`
Length = `20 cm`

Explanation:

Set:
`x =`width
`y =`length

Translate words into equations:
Equation 1: `"length" = 2xx"width" + 12 " " → y = 2x + 12`
Equation 2:`" perimeter" = 2xx"width" + 2xx"length " → 48 = 2x + 2y`

Insert equation 1 into equation 2
`48 = 2x + 2y`
`48 = 2x + 2(2x + 12)`
`48 = 2x + 4x +24`
`24 = 6x`
`x = 4 cm`

Find y through equation 1
`y = 2x + 12`
`y = 2xx4 + 12`
`y = 20 cm`

Answer 3

The width is `4 cm` and the length is `20cm`

Explanation:

We are told how the length of the rectangle is related to the width, so we can use one variable to define both sides.

Let the width be `x`

The the length is `2x+12" "larr'12` more than twice the width'

The perimeter is the sum of two widths and two lengths.

`2(x) + 2(2x+12) = 48" "larr` write an equation

`2x+4x+24=48`

`6x=48-24`

`6x = 24`

`x=4`

The width is `4 cm` and the length is `20cm`