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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

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.

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.

Re: If the area of a rectangle is 40, which of the following cou
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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

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

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

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

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

1

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 Kr Datta | GMAT Q51 | CAT 99.98 | Personalized Private Tutoring | Mentor & Coach | IIT (Indian Institute of Technology) alumnus

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Email: sujoy.datta@gmail.com | Whats-App: +919433063089

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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Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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