# 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?

Feb 14, 2016

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 $5 t$ ft and length be $6 t$ ft for some $t$.

The area is $270 = \left(5 t\right) \left(6 t\right) = 30 {t}^{2}$

Divide both ends by $30$ to find:

${t}^{2} = 9$

Hence $t = \pm 3$

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 $5 t = 15$ ft and length $6 t = 18$ ft.