NEW HERE? LEARN MORE
closeclose
Last visit was: 25 Apr 2024, 12:46 It is currently 25 Apr 2024, 12:46
Decision Tracker
My Rewards
New posts
New comers' posts

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

What is the perimeter of an equilateral triangle inscribed

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
avatar
arthuro69
Intern
Intern
Joined: 16 Apr 2012
Posts: 6
Own Kudos [?]: 25 [12]
Given Kudos: 3
Send PM
What is the perimeter of an equilateral triangle inscribed [#permalink] New post   Updated on: 09 Aug 2012, 15:05
3
Kudos
9
Bookmarks
00:00
A
B
C
D
E

Difficulty:

45% (medium)

Question Stats:

68% (01:56) correct 32% (02:06) wrong based on 308 sessions
Hide Show timer Statistics
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
ShowHide Answer
Official Answer
D

Originally posted by arthuro69 on 09 Aug 2012, 13:06.
Last edited by Bunuel on 09 Aug 2012, 15:05, edited 1 time in total.
Renamed the topic and edited the question.
Most Helpful Reply
User avatar
L
BrentGMATPrepNow
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6820
Own Kudos [?]: 29930 [8]
Given Kudos: 799
Location: Canada
Send PM
What is the perimeter of an equilateral triangle inscribed [#permalink] New post   Updated on: 04 Jun 2021, 11:41
3
Kudos
4
Bookmarks
Expert Reply
Top Contributor
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. \(24\)


So, here's what the diagram looks like.


If we draw lines from the center to each vertex, we get the following:


Since the radii have length 4, we can add that here:


Now we'll draw a line from the center that is PERPENDICULAR to one side of the tirangle.

We now have a SPECIAL 30-60-90 right triangle.

Here's the base version of this SPECIAL TRIANGLE


We can see that the each 30-60-90 triangle in the diagram is TWICE as big as the base version. So, each side opposite the 60º angle must have length 2√3


This means ONE side of the equilateral triangle has length 4√3, so the PERIMETER = 4√3 + 4√3 + 4√3 = 12√3

Answer: C

Cheers,
Brent

Originally posted by BrentGMATPrepNow on 19 Apr 2018, 14:23.
Last edited by BrentGMATPrepNow on 04 Jun 2021, 11:41, edited 1 time in total.
General Discussion
User avatar
G
mikemcgarry
Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4452
Own Kudos [?]: 28572 [2]
Given Kudos: 130
Re: What is the perimeter of an equilateral triangle inscribed [#permalink] New post   09 Aug 2012, 16:29
1
Kudos
1
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


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:
https://magoosh.com/gmat/2012/the-gmats- ... triangles/

Let me know if there are any further questions.

Mike :-)
Attachments

perimeter of an equilateral triangle inscribed in a circle of radius 4.pdf [168.07 KiB]
Downloaded 1106 times

avatar
venuvm
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] New post   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).
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92915
Own Kudos [?]: 619008 [3]
Given Kudos: 81595
Send PM
CAT Tests Forum Quiz Mode
Re: What is the perimeter of an equilateral triangle inscribed [#permalink] New post   04 Sep 2012, 03:32
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
anujbansal
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] New post   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
User avatar
S
thelion10
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] New post   16 Jul 2019, 10:45
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.
User avatar
B
adityasuresh
Manager
Manager
Joined: 03 May 2020
Posts: 108
Own Kudos [?]: 33 [0]
Given Kudos: 512
Send PM
Re: What is the perimeter of an equilateral triangle inscribed [#permalink] New post   08 Mar 2023, 06:00
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 2452 times ]

GMAT Club Bot
gmatclubot
Re: What is the perimeter of an equilateral triangle inscribed [#permalink]
08 Mar 2023, 06:00
Moderators:
Bunuel
Math Expert
92914 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions