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If the area of a rectangle is equal to the area of a square, then the

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Math Expert
Joined: 02 Sep 2009
Posts: 47920
If the area of a rectangle is equal to the area of a square, then the  [#permalink]

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22 Oct 2017, 06:08
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25% (medium)

Question Stats:

70% (01:13) correct 30% (00:40) wrong based on 82 sessions

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If the area of a rectangle is equal to the area of a square, then the perimeter of the rectangle must be

(A) one half of the perimeter of the square
(B) equal to the perimeter of the square
(C) equal to twice the perimeter of the square
(D) equal to the square root of the perimeter of the square
(E) none of the above

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Joined: 29 Aug 2017
Posts: 35
Re: If the area of a rectangle is equal to the area of a square, then the  [#permalink]

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22 Oct 2017, 06:22
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Bunuel wrote:
If the area of a rectangle is equal to the area of a square, then the perimeter of the rectangle must be

(A) one half of the perimeter of the square
(B) equal to the perimeter of the square
(C) equal to twice the perimeter of the square
(D) equal to the square root of the perimeter of the square
(E) none of the above

Area of a rectangle = Area of a square
lb = s*s
Perimeter of the square = 4s = $$4\sqrt{lb}$$
Perimeter of the rectangle = 2l + 2b which can't be expressed just in terms of the perimeter of the square

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Re: If the area of a rectangle is equal to the area of a square, then the  [#permalink]

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25 Oct 2017, 12:57
Bunuel, besides you who can I follow to get new quant questions on a regular basis?

E, for this one I plugged in numbers. A square with sides of 4, a rectangle with a length of 2 and width of 8. I then check my numbers with a square with sides of 10 and rectangle with a length of 4 and width of 25. The ratios of the perimeter were different, but I went ahead and checked the answer anyway.
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Posts: 47920
Re: If the area of a rectangle is equal to the area of a square, then the  [#permalink]

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25 Oct 2017, 22:40
Plunkster82 wrote:
Bunuel, besides you who can I follow to get new quant questions on a regular basis?

You can subscribe to any forum you want by clicking FOLLOW:
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Hope it helps.
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Re: If the area of a rectangle is equal to the area of a square, then the  [#permalink]

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30 Oct 2017, 13:57
Bunuel wrote:
If the area of a rectangle is equal to the area of a square, then the perimeter of the rectangle must be

(A) one half of the perimeter of the square
(B) equal to the perimeter of the square
(C) equal to twice the perimeter of the square
(D) equal to the square root of the perimeter of the square
(E) none of the above

Let’s say the rectangle has dimensions 2 and 8, and the square has a side length of 4. Each shape has an area of 16. The perimeter of the rectangle is 2(2 + 8) = 20 and that of the square is 4(4) = 16. We see that none of choices A to D are correct, so the correct answer is choice E.

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Re: If the area of a rectangle is equal to the area of a square, then the &nbs [#permalink] 30 Oct 2017, 13:57
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