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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]

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09 Aug 2012, 13:06
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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. $$24$$

[Reveal] Spoiler: OA

Last edited by Bunuel on 09 Aug 2012, 15:05, edited 1 time in total.
Renamed the topic and edited the question.
Magoosh GMAT Instructor
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Re: What is the perimeter of an equilateral triangle inscribed [#permalink]

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09 Aug 2012, 16:29
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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. $$24$$

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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Mike McGarry
Magoosh Test Prep

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Re: What is the perimeter of an equilateral triangle inscribed [#permalink]

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04 Sep 2012, 03:29
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]

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04 Sep 2012, 03:32
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. $$24$$

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]

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06 Jul 2014, 05:49
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Re: What is the perimeter of an equilateral triangle inscribed [#permalink]

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06 Jul 2014, 11:30
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, 11:30
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