# A rectangle has sides of lengths x and 2x. How do you express the area A of the rectangle as a function of it perimeter P?

Aug 14, 2017

The area $A$ of the rectangle as a function of it perimeter $P$ is ${P}^{2} / 18$.

#### Explanation:

As the sides of rectangle are $x$ and $2 x$, its perimeter $P$ is given by P=2×(x+2x)=6x.

or $x = \frac{1}{6} P = \frac{P}{6}$

Area of rectangle $A$ is x×2x=2x^2=2×(P/6)^2=2×P^2/36=P^2/18.

Hence the area $A$ of the rectangle as a function of it perimeter $P$ is ${P}^{2} / 18$.