# The width of a rectangle is 1/3 its length, l Which expression represents the perimeter of the rectangle?

Dec 1, 2016

$\frac{8 l}{3}$

#### Explanation:

Let the length of the rectangle be $l$

Then we can say that the width is $\frac{1}{3} \cdot l = \frac{l}{3}$

Now we need to form an expression (equation) for the perimeter.For that, we use the formula

color(blue)("Perimeter of a rectangle"=2(l+w) color(blue)("units"

Where,

$l = \text{length}$

$w = \text{width}$

We know that the length is $l$ and the width is $\frac{l}{3}$.Let's put it into the formula

$\rightarrow 2 \left(l + w\right)$

$\rightarrow 2 \left(l + \frac{l}{3}\right)$

Use the distributive formula color(brown)(a(b+c)=ab+ac

$\rightarrow 2 l + \frac{2 l}{3}$

$\rightarrow \frac{6 l}{3} + \frac{2 l}{3}$

color(green)(rArr(8l)/3

So, we can say that, the perimeter of the rectangle is $\frac{8 l}{3}$