Last visit was: 23 Apr 2026, 20:42 It is currently 23 Apr 2026, 20:42
Home
Messages
Tests
Schools
Events
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
Back to Forum
Create Topic
505-555 (Easy)|   Geometry|      
User avatar
siddhans
User avatar
Joined: 29 Jan 2011
Last visit: 04 Sep 2012
Posts: 152
Own Kudos:
802
 [5]
Given Kudos: 87
Posts: 152
Kudos: 802
 [5]
In the figure shown, the length of line segment QS is Updated on: 14 Oct 2019, 07:56
Originally posted by siddhans on 23 Jul 2011, 20:47.
Last edited by Bunuel on 14 Oct 2019, 07:56, edited 4 times in total.
Edited the question and added the OA
Kudos
Add Kudos
5
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

15% (low)

Question Stats:

77% (01:12) correct 23% (01:46) wrong based on 455 sessions

History

Date
Time
Result
Not Attempted Yet

In the figure shown, the length of line segment QS is \(4\sqrt{3}\). What is the perimeter of equilateral triangle PQR?

A. \(12\)
B. \(12 \sqrt{3}\)
C. \(24\)
D. \(24 \sqrt{3}\)
E. \(48\)

Show SpoilerWhat am i doing wrong here ?
Attachment:
Triangle.png
Triangle.png [ 9.81 KiB | Viewed 24404 times ]
What am i doing wrong here ?

PQ^2 = QS^2 + PS^2

PQ^2 = PS^2 + 48 ------ (1)

QR^2 = SR^2 + 48 ------(2)

Adding 1 and 2


PQ^2 + QR^2 = PS^2 + SR ^2 + 96 ----- 3

But, PS^2 + SR ^2 = PR ^2 ------- 4

Substitute 4 in 3....

PQ^2 + QR^2 = PR^2 + 96 -----5

PQ = PR = QR since equilateral triangle

Therefore PQ^2 = 96


PQ = sqrt (96)


But this doesnt yield the correct answer ....
ShowHide Answer
Official Answer
C
Need more similar questions? Run a 5 to 10 question quiz in GMAT Club Forum Quiz →
Most Helpful Reply
User avatar
BrentGMATPrepNow
User avatar
Major Poster
Joined: 12 Sep 2015
Last visit: 31 Oct 2025
Posts: 6,733
Own Kudos:
36,451
 [2]
Given Kudos: 799
Location: Canada
Expert
Expert reply
Posts: 6,733
Kudos: 36,451
 [2]
In the figure shown, the length of line segment QS is 19 Dec 2018, 09:39
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
siddhans
Attachment:
Triangle.png
In the figure shown, the length of line segment QS is \(4\sqrt{3}\). What is the perimeter of equilateral triangle PQR?

A. \(12\)
B. \(12 \sqrt{3}\)
C. \(24\)
D. \(24 \sqrt{3}\)
E. \(48\)
Show more

Let's first add the given information to the diagram.
If ∆PQR is an equilateral triangle, then the 3 angles are each 60°


At this point, we can see we have a special 30-60-90 right triangle, which we can compare with the BASE 30-60-90 right triangle


When we compare the sides that are opposite the 60° angle, we can see that 4√3 is 4 times the value of √3
So, the magnification factor is 4.
This means the other 2 lengths will be 4 times the sides of the BASE 30-60-90 right triangle


Now that we know that each side has length 8, the perimeter = 8 + 8 + 8 = 24

Answer: C

Cheers,
Brent
General Discussion
User avatar
agdimple333
User avatar
Joined: 24 Mar 2011
Last visit: 13 Aug 2013
Posts: 226
Own Kudos:
821
Given Kudos: 20
Location: Texas
Posts: 226
Kudos: 821
In the figure shown, the length of line segment QS is 23 Jul 2011, 21:08
Kudos
Add Kudos
Bookmarks
Bookmark this Post
siddhans
https://img210.imageshack.us/img210/3589/gmatprepr.jpg



Show SpoilerWhat am i doing wrong here ?
What am i doing wrong here ?




PQ^2 = QS^2 + PS^2

PQ^2 = PS^2 + 48 ------ (1)

QR^2 = SR^2 + 48 ------(2)

Adding 1 and 2


PQ^2 + QR^2 = PS^2 + SR ^2 + 96 ----- 3

But, PS^2 + SR ^2 = PR ^2 ------- 4

Substitute 4 in 3....

PQ^2 + QR^2 = PR^2 + 96 -----5

PQ = PR = QR since equilateral triangle

Therefore PQ^2 = 96


PQ = sqrt (96)


But this doesnt yield the correct answer ....
Show more

Red bold is not true... PS+SR = PR... so if you square (PS+SR)^2 = PR2... not what you have written

simplest way to solve this problem is sin60 = \(\sqrt{3}\)/2 = QS/PQ = 4\(\sqrt{3}\)/PQ
==> PQ = 8
so perimeter = 24
choice C.
User avatar
Impenetrable
User avatar
Joined: 14 Dec 2011
Last visit: 09 Feb 2014
Posts: 48
Own Kudos:
394
Given Kudos: 24
GMAT 1: 630 Q48 V29
GMAT 2: 690 Q48 V37
GMAT 2: 690 Q48 V37
Posts: 48
Kudos: 394
In the figure shown, the length of line segment QS is 21 Mar 2012, 04:07
Kudos
Add Kudos
Bookmarks
Bookmark this Post
agdimple333 is simple and easy. But how do I solve it without knowing sin (60)?
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 23 Apr 2026
Posts: 109,785
Own Kudos:
810,878
Given Kudos: 105,853
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,785
Kudos: 810,878
In the figure shown, the length of line segment QS is 21 Mar 2012, 04:34
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Impenetrable
agdimple333 is simple and easy. But how do I solve it without knowing sin (60)?
Show more

Trigonometry is not tested on the GMAT, which means that EVERY GMAT geometry question can be solved without it.

In the figure shown, the length of line segment QS is \(4\sqrt{3}\). What is the perimeter of equilateral triangle PQR?
A. \(12\)
B. \(12 \sqrt{3}\)
C. \(24\)
D. \(24 \sqrt{3}\)
E. \(48\)
Attachment:
Triangle.png
Triangle.png [ 9.81 KiB | Viewed 21261 times ]

Since triangle PQR is equilateral then its all angles equal to 60°. So, right triangle QSR is a 30°-60°-90° right triangle (with angle R equal to 60°). Next, in a right triangle where the angles are 30°, 60°, and 90° the sides are always in the ratio \(1 : \sqrt{3}: 2\) and the leg opposite 60° (QS) corresponds with \(\sqrt{3}\), which makes QR equal to \(4\sqrt{3}*\frac{2}{\sqrt{3}}=8\) (\(\frac{QS}{QR}=\frac{\sqrt{3}}{2}\) --> \(QR=QS*\frac{2}{\sqrt{3}}=8\)).

Thus the perimeter is 3*8=24.

Answer: C.

For more on this subject check Triangles chapter of Math Book: math-triangles-87197.html

Hope it helps.
avatar
saiesta
avatar
Joined: 03 Jan 2015
Last visit: 15 Nov 2018
Posts: 59
Own Kudos:
320
 [4]
Given Kudos: 146
Posts: 59
Kudos: 320
 [4]
In the figure shown, the length of line segment QS is 10 Feb 2016, 09:35
2
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Here is how I solved it.

An equilateral triangle has 3 equal sides, thus each angle is 60 degrees. Equilateral PQR has a line right down the middle, dividing the triangle PQR into two separate 30-60-90 triangles.



The properties of the 30-60-90 triangles are as follows:
Side with an angle of 30 degrees has a side length of \(x\)
Side with an angle of 60 degrees has a side length of \(x\sqrt{3}\)
Side with an angle of 90 degrees has a side length of \(2x\)

Knowing that \(4\sqrt{3}\) = \(x\sqrt{3}\) -----> \(4 = x\) (the side length of the 60 degree angle), you can easily calculate the rest of the other sides of the triangle.
So, putting it all together the perimeter of Equilateral PQR (see attached figure) = \(8 + 8 + 4 + 4 = 24\)
Attachments

Capturegmat.JPG
Capturegmat.JPG [ 19.37 KiB | Viewed 14905 times ]

User avatar
shasadou
User avatar
Joined: 12 Aug 2015
Last visit: 24 Nov 2022
Posts: 219
Own Kudos:
3,179
 [1]
Given Kudos: 1,475
Concentration: General Management, Operations
Schools: Johnson '18 (WL) Duke '18 (M) Tuck '18 (D)
GMAT 1: 640 Q40 V37
GMAT 2: 650 Q43 V36
GMAT 3: 600 Q47 V27
GPA: 3.3
WE:Management Consulting (Consulting)
Schools: Johnson '18 (WL) Duke '18 (M) Tuck '18 (D)
GMAT 3: 600 Q47 V27
Posts: 219
Kudos: 3,179
 [1]
In the figure shown, the length of line segment QS is 19 Apr 2016, 06:31
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Height in a an equilateral triangle equals \(\sqrt{3}\)/2 *a, where a is a side of such triangle. Hence a = \(\sqrt{3}\)/2 * a = 4\(\sqrt{3}\)
User avatar
Abhishek009
User avatar
Board of Directors
Joined: 11 Jun 2011
Last visit: 17 Dec 2025
Posts: 5,903
Own Kudos:
5,452
 [1]
Given Kudos: 463
Status:QA & VA Forum Moderator
Location: India
GPA: 3.5
WE:Business Development (Commercial Banking)
Posts: 5,903
Kudos: 5,452
 [1]
In the figure shown, the length of line segment QS is 19 Apr 2016, 08:30
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
siddhans
Attachment:
Triangle.png
In the figure shown, the length of line segment QS is \(4\sqrt{3}\). What is the perimeter of equilateral triangle PQR?

A. \(12\)
B. \(12 \sqrt{3}\)
C. \(24\)
D. \(24 \sqrt{3}\)
E. \(48\)

Show more

Altitude of a equilateral triangle is \({\sqrt{3} * side}/2\)

\({\sqrt{3} * side}/2\) = \(4\sqrt{3}\).

So sides are 8

Perimeter of an equilateral triangle is 3* sides = 3*8 =>24

Hence answer is (C)
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,960
Own Kudos:
1,117
Posts: 38,960
Kudos: 1,117
In the figure shown, the length of line segment QS is 15 Aug 2023, 12:39
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.
Moderators:
Bunuel
Math Expert
109785 posts
Krunaal
Tuck School Moderator
853 posts