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The average length of all the sides of a rectangle equals

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The average length of all the sides of a rectangle equals

by M7MBA » Tue Nov 14, 2017 6:01 am
The average length of all the sides of a rectangle equals twice the width of the rectangle. If the area of the rectangle is 18, what is its perimeter?
$$(A)\ 6\sqrt{6}$$
$$(B)\ 8\sqrt{6}$$
$$(C)\ 24$$
$$(D)\ 32$$
$$(E)\ 48$$

The OA is B.

What are the calculations behind this Ps question? Experts, could you show me how to determine the answer?
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by EconomistGMATTutor » Tue Nov 14, 2017 7:14 am
Hello M7MBA.

Let's take a look at your question. We have the next rectangle:

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The area of the rectangle is 18, that is to say, $$x\cdot y=18.$$. Also, "the average length of all the sides of a rectangle equals twice the width of the rectangle" means $$\frac{x+y+x+y}{4}=\frac{2x+2y}{4}=\frac{x+y}{2}=2\cdot y.$$

We can rewrite this last equation as follows: $$x+y=4y\ <-->\ x=3y.$$

If we replace this last equation in the area equation we will get: $$x\cdot y=18<-->\ 3y\cdot y=18<-->y^2=6<-->\ y=\sqrt{6}.$$

This implies that $$x=3\sqrt{6}.$$ and the perimeter is equal to $$2x+2y=6\sqrt{6}+2\sqrt{6}=8\sqrt{6}.$$

So, the correct answer is B.

I hope this can help you to understand the calculus.

I'm available if you'd like a follow up.

Regards.
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by Scott@TargetTestPrep » Sun Oct 20, 2019 9:12 am
M7MBA wrote:The average length of all the sides of a rectangle equals twice the width of the rectangle. If the area of the rectangle is 18, what is its perimeter?
$$(A)\ 6\sqrt{6}$$
$$(B)\ 8\sqrt{6}$$
$$(C)\ 24$$
$$(D)\ 32$$
$$(E)\ 48$$

The OA is B.

What are the calculations behind this Ps question? Experts, could you show me how to determine the answer?
We can let L = the length and W = the width of the rectangle. We can create the equation:

(2L + 2W)/4 = 2W

2L + 2W = 8W

2L = 6W

L = 3W

Since the area of the rectangle is 18, we have:

L * W = 18

3W * W = 18

3W^2 = 18

W^2 = 6

W = √6

Therefore, the perimeter of the rectangle is:

2L + 2W = 2(3√6) + 2(√6) = 6√6 + 2√6 = 8√6

Answer: B

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