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If the circumference of a certain circle is equal in length to the per

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Bunuel
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If the circumference of a certain circle is equal in length to the per [#permalink] New post   25 May 2021, 07:30
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If the circumference of a certain circle is equal in length to the perimeter of a certain square, what is the length of the side of the square in terms of d, the diameter of the circle?


A. \(\frac{\pi d}{2}\)

B. \(d\sqrt{2}\)

C. \(\frac{\pi d}{2\sqrt{2}}\)

D. \(\frac{\pi d}{4}\)

E. \(\frac{d}{\sqrt{2}}\)
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Re: If the circumference of a certain circle is equal in length to the per [#permalink] New post   25 May 2021, 08:02
Circumference = Pi x D = 4 L

L = Pi x D / 4
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Re: If the circumference of a certain circle is equal in length to the per [#permalink] New post   25 May 2021, 10:54
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Given,
Diameter of the circle = d
⟹ radius of the circle = \(\frac{d}{2}\)
Therefore, circumference of the circle = 2π \(\frac{d}{2}\)= πd

Let the length of each side of the square be a.
Then, the perimeter of the square = 4a

According to the problem, we have
circumference of the circle = perimeter of the square
πd=4a ⟹ a= \(\frac{πd}{4}\)

Hence, the correct answer is Option D.
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Re: If the circumference of a certain circle is equal in length to the per [#permalink] New post   25 May 2021, 13:09
Bunuel wrote:
If the circumference of a certain circle is equal in length to the perimeter of a certain square, what is the length of the side of the square in terms of d, the diameter of the circle?


A. \(\frac{\pi d}{2}\)

B. \(d\sqrt{2}\)

C. \(\frac{\pi d}{2\sqrt{2}}\)

D. \(\frac{\pi d}{4}\)

E. \(\frac{d}{\sqrt{2}}\)


Let S be one of the sides of a square
Given: \(2πr = 4S\)
\(πd = 4S\)(As 2Radius = Diameter)
\(\frac{πd}{4} = S\) - (D)
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Re: If the circumference of a certain circle is equal in length to the per [#permalink]
25 May 2021, 13:09
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