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# What is the perimeter of an equilateral triangle inscribed

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Intern
Joined: 16 Apr 2012
Posts: 8

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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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35% (medium)

Question Stats:

67% (01:11) correct 33% (01:28) wrong based on 118 sessions

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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.

Kudos [?]: 10 [1], given: 3

Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4373

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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

Kudos [?]: 8190 [1], given: 100

Intern
Joined: 03 Oct 2010
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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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Math Expert
Joined: 02 Sep 2009
Posts: 41714

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

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04 Sep 2012, 03:32
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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GMAT Club Legend
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Re: What is the perimeter of an equilateral triangle inscribed [#permalink]

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06 Jul 2014, 05:49
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Intern
Joined: 11 Nov 2013
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GMAT 1: 680 Q50 V31
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

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Re: What is the perimeter of an equilateral triangle inscribed   [#permalink] 06 Jul 2014, 11:30
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