# The length of a rectangle is four times its width. If the area of the rectangle is 256m^2 how do you find its perimeter?

Apr 6, 2018

The perimeter of the rectangle is $80$ meters.

#### Explanation:

Here are two formulas for rectangles that we will need to solve this problem, where $l$ = length and $w$ = width: (pinterest.com)

In this question, we know that:
$l = 4 w$
$A = 256 {m}^{2}$

First, let's find the width:
$l w = 256$

Let's substitute the value of $4 w$ for $l$:
$\left(4 w\right) w = 256$

Multiply the $w$:
$4 {w}^{2} = 256$

Divide both sides by $4$:
${w}^{2} = 64$

$w = 8$

So we know that the width is $8$.

Since $l = 4 w$ and we have $w$, we can find the value of $l$:
$4 \left(8\right)$
$32$

The width is $8$ meters and the length is $32$ meters.

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Now we find the perimeter. Remember the formula for the perimeter is $2 l + 2 w$ as stated earlier. Since we have the values of $l$ and $w$, we can solve this:
$2 \left(32\right) + 2 \left(8\right)$
$64 + 16$
$80$

The perimeter of the rectangle is $80$ meters.

Hope this helps!