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?

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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?

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Answer 1 · 2018-04-06T19:21:47

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:

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(pinterest.com)

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

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

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

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

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

$w = 8$

So we know that the width is $8$ .

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

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

$-------------------$

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

The perimeter of the rectangle is $80$ meters.

Hope this helps!

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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?

1 Answer

Explanation:

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