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# The perimeter of a square with a side of length S is equal to the circ

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SVP
Joined: 12 Dec 2016
Posts: 1710
Location: United States
GMAT 1: 700 Q49 V33
GPA: 3.64
The perimeter of a square with a side of length S is equal to the circ  [#permalink]

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04 Jan 2018, 02:27
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Difficulty:

25% (medium)

Question Stats:

82% (01:21) correct 18% (02:17) wrong based on 30 sessions

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The perimeter of a square with a side of length S is equal to the circumference of a circle. In terms of S, what is the area of the circle?

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Joined: 02 Sep 2009
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Re: The perimeter of a square with a side of length S is equal to the circ  [#permalink]

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04 Jan 2018, 02:35
chesstitans wrote:
The perimeter of a square with a side of length S is equal to the circumference of a circle. In terms of S, what is the area of the circle?

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b.JPG

The perimeter of a square with a side of length S is 4S. So, we are told that $$4S=2\pi r$$ for a certain circle.

$$4S=2\pi r$$;

$$r=\frac{2S}{\pi}$$

$$area_{circle} = \pi r^2 = \pi *(\frac{2S}{\pi})^2=\frac{4S^2}{\pi}$$.

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Re: The perimeter of a square with a side of length S is equal to the circ &nbs [#permalink] 04 Jan 2018, 02:35
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# The perimeter of a square with a side of length S is equal to the circ

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