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If the area of a rectangle is 40, which of the following cou
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19 May 2017, 02:19

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Question Stats:

If the area of a rectangle is 40, which of the following could be the perimeter of the rectangle?

Indicate all such perimeters.

❑ 20

❑ 40

❑ 200

❑ 400

❑ 2,000

❑ 4,000

_________________

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Re: If the area of a rectangle is 40, which of the following cou
[#permalink]
17 Jul 2017, 07:33

2

Expert Reply

OE

The perimeter of a rectangle whose area is 40 can be as large as we like (for example, if the length is 4,000 and the width is 0.01, the perimeter is 8,000.02). However, the perimeter is the smallest when the rectangle is a square, in which case each side is \(\sqrt{40}\) and the perimeter is 4 \(\sqrt{40}\). Since \(\sqrt{40}\) > 6, the perimeter is greater than 4 x 6.24. So Choice A, 20, is not possible All of the other choices are possible.

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The perimeter of a rectangle whose area is 40 can be as large as we like (for example, if the length is 4,000 and the width is 0.01, the perimeter is 8,000.02). However, the perimeter is the smallest when the rectangle is a square, in which case each side is \(\sqrt{40}\) and the perimeter is 4 \(\sqrt{40}\). Since \(\sqrt{40}\) > 6, the perimeter is greater than 4 x 6.24. So Choice A, 20, is not possible All of the other choices are possible.

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Re: If the area of a rectangle is 40, which of the following cou
[#permalink]
04 Aug 2019, 13:18

Is there another way to approach this?

Re: If the area of a rectangle is 40, which of the following cou
[#permalink]
04 Aug 2019, 16:57

1

Expert Reply

1

Bookmarks

\(40 = 2^3 \times 5\)

which is \(8 \times 5\)

Now, if you consider that 8+5=13 and the perimeter is \(13 \times 2= 26\)

The perimeter is at the very least 26 or above.

20 is impossible

So A is wrong and all the other choices are.

Regards

_________________

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which is \(8 \times 5\)

Now, if you consider that 8+5=13 and the perimeter is \(13 \times 2= 26\)

The perimeter is at the very least 26 or above.

20 is impossible

So A is wrong and all the other choices are.

Regards

_________________

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GRE: All you do need to know about the GRE Test | GRE Prep Club for the GRE Exam - The Complete FAQ

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Posting Rules: QUANTITATIVE | VERBAL

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ETS: ETS Free PowerPrep 1 & 2 All 320 Questions Explanation. | ETS All Official Guides

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Scores: The GRE average score at Top 25 Business Schools 2020 Ed. | How to study for GRE retake and score HIGHER - (2020)

How is the GRE Score Calculated -The Definitive Guide (2021)

Tests: GRE Prep Club Tests | FREE GRE Practice Tests [Collection] - New Edition (2021)

Vocab: GRE Prep Club Official Vocabulary Lists for the GRE (2021)

Re: If the area of a rectangle is 40, which of the following cou
[#permalink]
22 Jan 2020, 21:09

As mentioned by others. The key to solving this question quickly is that given an area for a rectangle the perimeter is always minimized when the rectangle is a square. This will happen when length and width are the same. Since lw=40 this means l=rad(40) and w=rad(40) and the smallest perimeter possible is 4rad(40) which is around 25.3 if you plug it in the calculator. So 20 is the only one below that.

Everything about 25.3 will be valid since we can let the width be literally any positive number and adjust the length to make it area 40, therefore the perimeter itself is unbounded above.

Everything about 25.3 will be valid since we can let the width be literally any positive number and adjust the length to make it area 40, therefore the perimeter itself is unbounded above.

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Re: If the area of a rectangle is 40, which of the following cou
[#permalink]
23 Jan 2020, 00:53

4

1

Question)

If the area of a rectangle is 40, which of the following could be the perimeter of the rectangle? Indicate all such perimeters.

❑ 20

❑ 40

❑ 200

❑ 400

❑ 2,000

❑ 4,000

Solution:

Since the area of the rectangle is 40, possible cases are:

#1. L x W = 40 x 1 => Perimeter = 2(40 + 1) = 82

#2. L x W = 20 x 2 => Perimeter = 2(20 + 2) = 44

#3. L x W = 8 x 5 => Perimeter = 2(8 + 5) = 26

We can observe that closer the values of L and W, smaller the perimeter of the rectangle.

Thus, the minimum perimeter would be when L = W

=> L = W = \(\sqrt{40}\) = 6.32

=> Perimeter = 2(6.32 + 6.32) = 25.3

Thus, the minimum perimeter is 25.3

Thus, any value of the perimeter higher than 25.3 is possible.

For example, if you are thinking how the perimeter can have such large values as mentioned in the last two options:

We can assume the length as 2000 and then the width becomes 40/2000 = 0.02

=> Perimeter = 2(2000 + 0.02) = 4000.04

Answer: B, C, D, E, F

_________________

If the area of a rectangle is 40, which of the following could be the perimeter of the rectangle? Indicate all such perimeters.

❑ 20

❑ 40

❑ 200

❑ 400

❑ 2,000

❑ 4,000

Solution:

Since the area of the rectangle is 40, possible cases are:

#1. L x W = 40 x 1 => Perimeter = 2(40 + 1) = 82

#2. L x W = 20 x 2 => Perimeter = 2(20 + 2) = 44

#3. L x W = 8 x 5 => Perimeter = 2(8 + 5) = 26

We can observe that closer the values of L and W, smaller the perimeter of the rectangle.

Thus, the minimum perimeter would be when L = W

=> L = W = \(\sqrt{40}\) = 6.32

=> Perimeter = 2(6.32 + 6.32) = 25.3

Thus, the minimum perimeter is 25.3

Thus, any value of the perimeter higher than 25.3 is possible.

For example, if you are thinking how the perimeter can have such large values as mentioned in the last two options:

We can assume the length as 2000 and then the width becomes 40/2000 = 0.02

=> Perimeter = 2(2000 + 0.02) = 4000.04

Answer: B, C, D, E, F

_________________

Sujoy Kumar Datta | GMAT Q51 | CAT 99.98 | Mentor & Coach | IIT (Indian Institute of Technology) alumnus

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Re: If the area of a rectangle is 40, which of the following cou
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04 Jul 2021, 04:55

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