Question

The length of a rectangle is twice its width. If the area of the rectangle is 162in^2, find its perimeter.

Answer 1

We know that the length of a rectangle is twice its width. Then:

The area of a rectangle is the product of its width and length. Then:

`A=2x\cdot x=2x^2`

Additionally, we know that the area is 162 in². Using the expression above we can obtain the value of x:

`\begin{gathered} 162=2x^2 \\ 81=x^2 \\ x=9\text{ in} \end{gathered}`

Finally, the perimeter (2P) is just twice the sum of the width and the length of the rectangle:

`2P=2\cdot(2x+x)=6x=6\cdot9=54\text{ in}`