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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
19 May 2017, 02:19
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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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Official Answer
B,C,D,E,F
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Re: If the area of a rectangle is 40, which of the following cou
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23 Jan 2020, 00:53
23 Jan 2020, 00:53
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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
General Discussion
Re: If the area of a rectangle is 40, which of the following cou
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17 Jul 2017, 07:33
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.
