Last visit was: 12 Jul 2024, 20:58 It is currently 12 Jul 2024, 20:58
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Close
Request Expert Reply
Confirm Cancel
SORT BY:
Date
Tags:
Show Tags
Hide Tags
avatar
Intern
Intern
Joined: 16 Apr 2012
Posts: 6
Own Kudos [?]: 25 [12]
Given Kudos: 3
Send PM
Most Helpful Reply
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6805
Own Kudos [?]: 30789 [8]
Given Kudos: 799
Location: Canada
Send PM
General Discussion
Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4490
Own Kudos [?]: 28827 [2]
Given Kudos: 130
avatar
Intern
Intern
Joined: 03 Oct 2010
Posts: 3
Own Kudos [?]: [0]
Given Kudos: 2
Send PM
Re: What is the perimeter of an equilateral triangle inscribed [#permalink]
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).
Math Expert
Joined: 02 Sep 2009
Posts: 94302
Own Kudos [?]: 640202 [3]
Given Kudos: 84576
Send PM
Re: What is the perimeter of an equilateral triangle inscribed [#permalink]
1
Kudos
2
Bookmarks
Expert Reply
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.
avatar
Intern
Intern
Joined: 11 Nov 2013
Posts: 17
Own Kudos [?]: 16 [0]
Given Kudos: 17
GMAT 1: 680 Q50 V31
Send PM
Re: What is the perimeter of an equilateral triangle inscribed [#permalink]
Let x be the side of triangle.

Using cosine rule:
(x/2)/R = cos 30
=> x = 2Rcos 30 = 4√3
=> Perimeter = 3X = 12√3
Intern
Intern
Joined: 14 May 2019
Posts: 32
Own Kudos [?]: 48 [2]
Given Kudos: 41
Concentration: Technology, Strategy
Send PM
Re: What is the perimeter of an equilateral triangle inscribed [#permalink]
2
Bookmarks
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


way simpler to simply know a formula :

Whenever a Circle circumscribes an equilateral triangle, the The radius of the circle can be defined by : Radius = \(\frac{Side Of The Triangle}{\sqrt{3}}\).

that way, if we solve the problem : 4 = \(\frac{s}{\sqrt{3}}\) . Hence, side = \(4\sqrt{3}\).

Now, the perimeter = 3 x \(4\sqrt{3}\) = 12\(\sqrt{3}\) .
The answer is the option D.
Manager
Manager
Joined: 03 May 2020
Posts: 108
Own Kudos [?]: 35 [0]
Given Kudos: 512
Send PM
Re: What is the perimeter of an equilateral triangle inscribed [#permalink]
For equilateral triangle the radius of the circumscribed circle R = Side * \(Root 3/3\)
Attachments

File comment: PFA
833BE90B-5F55-4C0D-A36E-C4067598451A.jpeg
833BE90B-5F55-4C0D-A36E-C4067598451A.jpeg [ 403.97 KiB | Viewed 2678 times ]

GMAT Club Bot
Re: What is the perimeter of an equilateral triangle inscribed [#permalink]
Moderator:
Math Expert
94302 posts