Question

The area of a rectangle is 270 square feet. The ratio of the width to the length is 5:6. How do you find the length and the width?

Answer 1

Solve to find length `18` ft and width `15` ft.

Explanation:

Since we are told that the ratio of the width to the length is `5:6` then let the width be `5t` ft and length be `6t` ft for some `t`.

The area is `270 = (5t)(6t) = 30t^2`

Divide both ends by `30` to find:

`t^2 = 9`

Hence `t=+-3`

Since we're dealing with a real rectangle, we require `t > 0` so that the width and length are positive, so `t=3`

The width is then `5t = 15` ft and length `6t = 18` ft.