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What is the perimeter of an equilateral triangle inscribed

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What is the perimeter of an equilateral triangle inscribed [#permalink] New post 09 Aug 2012, 12:06
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67% (02:15) correct 33% (01:34) wrong based on 96 sessions
What is the perimeter of an equilateral triangle inscribed in a circle of radius 4 ?

A. 6\sqrt{2}
B. 6\sqrt{3}
C. 12\sqrt{2}
D. 12\sqrt{3}
E. 24

source: readyforgmat.com
[Reveal] Spoiler: OA

Last edited by Bunuel on 09 Aug 2012, 14:05, edited 1 time in total.
Renamed the topic and edited the question.
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Re: What is the perimeter of an equilateral triangle inscribed [#permalink] New post 09 Aug 2012, 15:29
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arthuro69 wrote:
What is the perimeter of an equilateral triangle inscribed in a circle of radius 4 ?

A. 6\sqrt{2}
B. 6\sqrt{3}
C. 12\sqrt{2}
D. 12\sqrt{3}
E. 24

source: readyforgmat.com


Hi, there. I'm happy to help. :-)

The full solution to the problem is in the attached pdf.

If the details of the 30-60-90 triangle are not familiar to you, I recommend brushing up with this post:
http://magoosh.com/gmat/2012/the-gmats- ... triangles/

Let me know if there are any further questions.

Mike :-)
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Re: What is the perimeter of an equilateral triangle inscribed [#permalink] New post 04 Sep 2012, 02:29
The radius of circum circle of an equilateral triangle = a/sqrt(3). a is the side of triangle.
Here: a/sqrt(3) = 4
a = 4*sqrt(3).
perimeter 3a = 3*4*sqrt(3) = 12sqrt(3).
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Re: What is the perimeter of an equilateral triangle inscribed [#permalink] New post 04 Sep 2012, 02:32
Expert's post
arthuro69 wrote:
What is the perimeter of an equilateral triangle inscribed in a circle of radius 4 ?

A. 6\sqrt{2}
B. 6\sqrt{3}
C. 12\sqrt{2}
D. 12\sqrt{3}
E. 24

source: readyforgmat.com


All you need to know about triangles for the GMAT: math-triangles-87197.html

Hope it helps.
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Re: What is the perimeter of an equilateral triangle inscribed [#permalink] New post 06 Jul 2014, 04:49
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Re: What is the perimeter of an equilateral triangle inscribed [#permalink] New post 06 Jul 2014, 10:30
Let x be the side of triangle.

Using cosine rule:
(x/2)/R = cos 30
=> x = 2Rcos 30 = 4√3
=> Perimeter = 3X = 12√3
Re: What is the perimeter of an equilateral triangle inscribed   [#permalink] 06 Jul 2014, 10:30
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