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ABCDE is a regular polygon of side 8 cm. What is the length

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Ravithj
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ABCDE is a regular polygon of side 8 cm. What is the length [#permalink] New post   Updated on: 23 Apr 2014, 00:00
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ABCDE is a regular polygon of side 8 cm. What is the length of diagonal AC(in cm)?

A. \(2(2+\sqrt{5})\)

B. \(4(2+\sqrt{3})\)

C. \(4(1+\sqrt{5})\)

D. \(\frac{16}{\sqrt{3}}\)

E. \(8(\sqrt{5}-1)\)

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Originally posted by Ravithj on 22 Apr 2014, 22:59.
Last edited by Bunuel on 23 Apr 2014, 00:00, edited 1 time in total.
Renamed the topic and edited the question.
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Re: ABCDE is a regular polygon of side 8 cm. What is the length [#permalink] New post   23 Apr 2014, 09:56
C it is.

Hint: sin54 = \(\frac{1+\sqrt{5}}{4}\)
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Re: ABCDE is a regular polygon of side 8 cm. What is the length [#permalink] New post   23 Apr 2014, 11:24
utkmittal1 wrote:
C it is.

Hint: sin54 = \(\frac{1+\sqrt{5}}{4}\)


is there a more GMAT like solution? because i don't get the reason to remember sin54! :(
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Re: ABCDE is a regular polygon of side 8 cm. What is the length [#permalink] New post   23 Apr 2014, 11:41
HBSdetermined wrote:
utkmittal1 wrote:
C it is.

Hint: sin54 = \(\frac{1+\sqrt{5}}{4}\)


is there a more GMAT like solution? because i don't get the reason to remember sin54! :(


I don't think GMAT will ever ask a question that will require you to remember the value of sin54. So be happy :)
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Re: ABCDE is a regular polygon of side 8 cm. What is the length [#permalink] New post   23 Apr 2014, 23:06
Golden Ratio \(= \frac{1 + \sqrt{5}}{2}\)

Length of diagonal of regular pentagon = 8 * Golden Ratio

\(= 4 (1 + \sqrt{5})\)

Answer = C

I really doubt if "Golden Ratio" concept is tested in GMAT?

Bunuel, any inputs please...
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Re: ABCDE is a regular polygon of side 8 cm. What is the length [#permalink] New post   24 Apr 2014, 01:38
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Ravithj wrote:
ABCDE is a regular polygon of side 8 cm. What is the length of diagonal AC(in cm)?

A. \(2(2+\sqrt{5})\)

B. \(4(2+\sqrt{3})\)

C. \(4(1+\sqrt{5})\)

D. \(\frac{16}{\sqrt{3}}\)

E. \(8(\sqrt{5}-1)\)


Not a GMAT question. You can ignore it.

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This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
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Thank you for understanding, and happy exploring!
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Re: ABCDE is a regular polygon of side 8 cm. What is the length [#permalink]
24 Apr 2014, 01:38
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