Question

A rectangular park has an area of `2/3` square mile. The length of the park is `2 2/3` the width of the park. What is the width of the park?

Answer 1

See a solution process below:

Explanation:

In the problem we are told the length is: `l = 2 2/3 xx w`

We can convert this to an improper fraction to make it easier to work with:

`2 2/3 = 2 + 2/3 = (2 xx 3/3) + 2/3 = 6/3 + 2/3 = (6 + 2)/3 = 8/3`

Therefore the length is: `l = 8/3w`

The formula for area of a rectangle is:

`A = l xx w` Where:

• `A` is the area of the rectangle: `2/3" square mile"` or `2/3"mi"^2` for this problem.

• `l` is the length of the rectangle: `8/3w` for this problem.

• `w` is the width of the rectangle. What we are solving for.

Substituting and solving for `w` gives:

`2/3"mi"^2 = 8/3w xx w`

`2/3"mi"^2 = 8/3w^2`

`color(red)(3)/color(blue)(8) xx 2/3"mi"^2 = color(red)(3)/color(blue)(8) xx 8/3w^2`

`cancel(color(red)(3))/color(blue)(8) xx 2/color(red)(cancel(color(black)(3)))"mi"^2 = cancel(color(red)(3))/cancel(color(blue)(8)) xx color(blue)(cancel(color(black)(8)))/color(red)(cancel(color(black)(3)))w^2`

`2/color(blue)(8)"mi"^2 = w^2`

`1/4"mi"^2 = w^2`

`sqrt(1/4"mi"^2) = sqrt(w^2)`

`sqrt(1/4)sqrt("mi"^2) = w`

`1/2"mi" = w`

`w = 1/2"mi"`

The width of the park is `1/2` mile.

The length of the park would be:

`l = 8/3 xx 1/2"mi" = (color(red)(cancel(color(black)(8)))4)/3 xx 1/color(red)(cancel(color(black)(2)))"mi" = 4/3"mi"`

`1/2"mi" xx 4/3"mi" = 1/color(red)(cancel(color(black)(2)))"mi" xx (color(red)(cancel(color(black)(4)))2)/3"mi" = 2/3"mi"^2`