Question

The length of a rectangle is twice its width. If the perimeter of the rectangle is 36m What is the area?

Answer 1

Area = `72m^2`

Explanation:

Perimeter of rectangle is `2l + 2w`

now `l=2 × w`
`l=2w`

Perimeter = `(2 × w) + (2 × 2w)`
Perimeter = `2w+4w`

`36=6w`

`w=36/6`

`w=6`

Hence, width = 6m.

Now Area of rectangle is `l w`

Since `w=6m`, length `l = 2w = 2×6 = 12m`

Area = `6 xx 12 = 72m^2`

Answer 2

`Area = 72 meters`²

Explanation:

This problem is confusing for a couple of reasons.

For one thing, it's hard to know how to write a math expression for "The length of a rectangle is twice its width."

For another thing, it gives you information about perimeter, but it wants an answer about area.

The trick is to proceed one step at a time.

`color(white)(mmmmmmmm)`―――――――――

Step 1:
Mathematically express the relationships among the dimensions.

Let `x` represent the number of meters in the width.

Width . . . . . . . . . . . . . . . `x` `larr` number of meters in the width
Twice this amount . . . `2x` `larr` number of meters in the length

[ Two widths ] plus [ two lengths ] equals the perimeter
[ `color(white)`    `2 (x)` `color(white)(mn`  ] `+` `color(white)(.)[     2 (2x)` `color(white)(nn` ]   `=`        `36 m`

`2x + 2(2x) = 36`

`color(white)(mmmmmmmm)`―――――――――

Step 2:
Solve for `x`
`x` is already defined as "the number of meters in the width"

`2x + 2(2x) = 36`

1) Clear the parentheses by distributing the `2`
`2x + 4x = 36`

2) Combine like terms
`6x = 36`

3) Divide both sides by `6` to isolate `x`, already defined as "the number of meters in the width"
`x = 6` `larr` the number of meters in the width

So the length, which is given as "twice as long," must be `12`

`color(white)(mmmmmmmm)`―――――――――

Step 3:
Use the dimensions of the rectangle to find its area

Area  is  width`×` length
`A      =   6m  ×   12m`

`Area = 72  meters²` `larr` answer