Last visit was: 24 Apr 2026, 13:49 It is currently 24 Apr 2026, 13:49
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
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 24 Apr 2026
Posts: 109,818
Own Kudos:
811,065
Given Kudos: 105,873
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: 109,818
Kudos: 811,065
If QR = 2, then what is the perimeter of quadrilateral PQRS in the fig 21 Feb 2018, 01:12
Kudos
Add Kudos
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
B
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:

80% (01:21) correct 20% (01:33) wrong based on 78 sessions

History

Date
Time
Result
Not Attempted Yet

If QR = 2, then what is the perimeter of quadrilateral PQRS in the figure above?

A. \(6\sqrt{2} + 4\)

B. \(4\sqrt{2} + 4\)

C. \(4\sqrt{2} + 2\)

D. \(2\sqrt{2} + 2\)

E. \(3\sqrt{2}\)

Show Spoiler
Attachment:
2018-02-21_1019_003.png
2018-02-21_1019_003.png [ 11.56 KiB | Viewed 2457 times ]
ShowHide Answer
Official Answer
B
User avatar
gmatexam439
User avatar
Moderator
Joined: 28 Mar 2017
Last visit: 18 Oct 2024
Posts: 1,054
Own Kudos:
2,195
Given Kudos: 200
Location: India
Concentration: Finance, Technology
Schools: McDonough '21 (A$) Jones '21 (A$) Kelley '23 (A)
GMAT 1: 730 Q49 V41
GPA: 4
Products:
My Reviews
Schools: McDonough '21 (A$) Jones '21 (A$) Kelley '23 (A)
GMAT 1: 730 Q49 V41
Posts: 1,054
Kudos: 2,195
If QR = 2, then what is the perimeter of quadrilateral PQRS in the fig 21 Feb 2018, 01:38
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel

If QR = 2, then what is the perimeter of quadrilateral PQRS in the figure above?

A. \(6\sqrt{2} + 4\)

B. \(4\sqrt{2} + 4\)

C. \(4\sqrt{2} + 2\)

D. \(2\sqrt{2} + 2\)

E. \(3\sqrt{2}\)

Show Spoiler
Attachment:
2018-02-21_1019_003.png
Show more

PR=\(2*\sqrt{2}\)
Perimeter = \(4*\sqrt{2}+4\)
User avatar
Hatakekakashi
User avatar
Joined: 07 Jan 2016
Last visit: 22 Feb 2025
Posts: 1,228
Own Kudos:
483
Given Kudos: 126
Location: United States (MO)
GMAT 1: 710 Q49 V36
Products:
My Reviews
GMAT 1: 710 Q49 V36
Posts: 1,228
Kudos: 483
If QR = 2, then what is the perimeter of quadrilateral PQRS in the fig 21 Feb 2018, 04:07
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel

If QR = 2, then what is the perimeter of quadrilateral PQRS in the figure above?

A. \(6\sqrt{2} + 4\)

B. \(4\sqrt{2} + 4\)

C. \(4\sqrt{2} + 2\)

D. \(2\sqrt{2} + 2\)

E. \(3\sqrt{2}\)

Show Spoiler
Attachment:
2018-02-21_1019_003.png
Show more

right angle triangle 90-45-45 ratio of sides 1:1:rt2

so side of equilateral traingle = 2 rt 2

perimited = 2+ 2 + 2rt2 + 2rt2

4rt2 + 4
(B) imo
avatar
ramblers
avatar
Joined: 21 Aug 2017
Last visit: 19 Oct 2018
Posts: 66
Own Kudos:
37
Given Kudos: 38
Location: United States
Schools: Oxford"20 (A)
GMAT 1: 700 Q43 V42
Schools: Oxford"20 (A)
GMAT 1: 700 Q43 V42
Posts: 66
Kudos: 37
If QR = 2, then what is the perimeter of quadrilateral PQRS in the fig 21 Feb 2018, 17:27
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Looks scary if you're inclined to hate geometry like myself, but quite simple when you remember rules and take good notes.

\(x^2+x^2=PR^2\), so \(2^2+2^2=8\)

From there, we know that \(PR=\sqrt{8}\). That can be simplified to \(2\sqrt{2}\).

Since all angles of triangle PRS = 60, we know that we have an equilateral triangle and all sides are a the same. We're looking for the perimeter of the whole quadrilateral, so side RS and SP will contribute to it. Those are both equal to PR, so we'll take 2 of those, or \(2*2\sqrt{2}\), or more simply, \(4\sqrt{2}\).

We're given that \(x=2\), and 2 of those contribute to the perimeter, so the final perimeter will be \(4+4\sqrt{2}\).

Answer choice B.
User avatar
rishabhmishra
User avatar
Joined: 23 Sep 2016
Last visit: 16 Aug 2019
Posts: 177
Own Kudos:
466
Given Kudos: 29
Products:
My Reviews
Posts: 177
Kudos: 466
If QR = 2, then what is the perimeter of quadrilateral PQRS in the fig 22 Feb 2018, 00:41
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel

If QR = 2, then what is the perimeter of quadrilateral PQRS in the figure above?

A. \(6\sqrt{2} + 4\)

B. \(4\sqrt{2} + 4\)

C. \(4\sqrt{2} + 2\)

D. \(2\sqrt{2} + 2\)

E. \(3\sqrt{2}\)

Show Spoiler
Attachment:
2018-02-21_1019_003.png
Show more
Answer must be B as x=2 and triangle QRS is isosceles then 3rd side is 2root 2 so perimeter is sum of all the side 2 sides with 2root 2 and 2 sides with 2 length so total is 4root2+ 4
User avatar
JeffTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 04 Mar 2011
Last visit: 05 Jan 2024
Posts: 2,974
Own Kudos:
8,711
Given Kudos: 1,646
Status:Head GMAT Instructor
Affiliations: Target Test Prep
Expert
Expert reply
Posts: 2,974
Kudos: 8,711
If QR = 2, then what is the perimeter of quadrilateral PQRS in the fig 26 Feb 2018, 10:47
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel

If QR = 2, then what is the perimeter of quadrilateral PQRS in the figure above?

A. \(6\sqrt{2} + 4\)

B. \(4\sqrt{2} + 4\)

C. \(4\sqrt{2} + 2\)

D. \(2\sqrt{2} + 2\)

E. \(3\sqrt{2}\)

Show Spoiler
Attachment:
2018-02-21_1019_003.png
Show more

Since triangle PQR is an isosceles right triangle, side PR = 2√2. Since triangle PRS is an equilateral triangle, PR = RS = PS = 2√2.

So the perimeter of quadrilateral PQRS is 2 + 2 + 2√2 + 2√2 = 4 + 4√2.

Answer: B
Moderators:
Bunuel
Math Expert
109818 posts
Krunaal
Tuck School Moderator
853 posts