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?
The average length of all the sides of a rectangle equals
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- EconomistGMATTutor
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Hello M7MBA.
Let's take a look at your question. We have the next rectangle:
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.
Let's take a look at your question. We have the next rectangle:
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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We can let L = the length and W = the width of the rectangle. We can create the equation: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?
(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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