Last visit was: 22 Sep 2026, 03:46 It is currently 22 Sep 2026, 03:46
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
705-805 (Hard)|   Geometry|      
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 22 Sep 2026
Posts: 113,752
Own Kudos:
842,868
 [19]
Given Kudos: 111,734
Products:
GMAT Club Tests
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 113,752
Kudos: 842,868
 [19]
What is the ratio of longest diagonal to the shortest diagonal in a re 01 May 2020, 03:49
Kudos
Add Kudos
19
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

75% (hard)

Question Stats:

55% (02:27) correct 45% (02:27) wrong based on 87 sessions

History

Date
Time
Result
Not Attempted Yet
What is the ratio of longest diagonal to the shortest diagonal in a regular octagon (an eight-sided polygon)?

A. 3 : 1
B. 2 : 1
C. √3 : 1
D. √2 : 1
E. 2 : √3

Are You Up For the Challenge: 700 Level Questions
ShowHide Answer
Official Answer
D
User avatar
ArunSharma12
User avatar
Joined: 25 Oct 2015
Last visit: 20 Jul 2022
Posts: 512
Own Kudos:
1,055
 [2]
Given Kudos: 74
Location: India
Schools: IIML-IPMX '22 (A)
GMAT 1: 650 Q48 V31
GMAT 2: 720 Q49 V38 (Online)
GPA: 4
Products:
My Reviews
Schools: IIML-IPMX '22 (A)
GMAT 2: 720 Q49 V38 (Online)
Posts: 512
Kudos: 1,055
 [2]
What is the ratio of longest diagonal to the shortest diagonal in a re 01 May 2020, 04:48
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
What is the ratio of longest diagonal to the shortest diagonal in a regular octagon (an eight-sided polygon)?

A. 3 : 1
B. 2 : 1
C. √3 : 1
D. √2 : 1
E. 2 : √3

Show more

regular octagon:
exterior angle = 360 /8 = 45
interior angle = 180 - 45 = 135
Attachment:
img.png
img.png [ 22.26 KiB | Viewed 12771 times ]
in the figure the two shortest diagonals will be same length x and longer diagonal be y.
as the triangle is right angled.
y = \(\sqrt{2}\)x
y/x = \(\sqrt{2}:1\)
Ans: D
User avatar
GMATinsight
User avatar
Major Poster
Joined: 08 Jul 2010
Last visit: 19 Sep 2026
Posts: 7,377
Own Kudos:
17,535
 [3]
Given Kudos: 128
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Products:
My Reviews
Expert
Expert reply
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
Posts: 7,377
Kudos: 17,535
 [3]
What is the ratio of longest diagonal to the shortest diagonal in a re 02 May 2020, 05:40
2
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Bunuel
What is the ratio of longest diagonal to the shortest diagonal in a regular octagon (an eight-sided polygon)?

A. 3 : 1
B. 2 : 1
C. √3 : 1
D. √2 : 1
E. 2 : √3

Are You Up For the Challenge: 700 Level Questions
Show more


Please enjoy the step-by-step approach in the video solution.

Answer: Option D

Please subscribe to the youtube channel if you like the video and enjoy more such videos for FREE


Attachments

GMATinsight Polygon.png
GMATinsight Polygon.png [ 829.33 KiB | Viewed 12204 times ]

User avatar
lacktutor
User avatar
Joined: 25 Jul 2018
Last visit: 23 Oct 2023
Posts: 658
Own Kudos:
1,497
 [2]
Given Kudos: 69
Posts: 658
Kudos: 1,497
 [2]
What is the ratio of longest diagonal to the shortest diagonal in a re 03 May 2020, 16:15
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Please See The Attached File.

If you draw this octagon inside the circle, the longest diagonal will 2R.
As you see the right-angled triangle in the picture, two other sides of the triangle is the shortest diagonal of the octagon.
---> \(x^{2} + x^{2} = (2R)^{2}\)

\(2x^{2} = 4R^{2}\)

\(x = √2R\)

\(\frac{Diagonal_{Longest}}{ Diagonal_{Shortest} }= \frac{2R}{√2R}= \frac{√2}{1}\)

Answer (D).
Attachments

Octagon.jpg
Octagon.jpg [ 52.02 KiB | Viewed 11451 times ]

avatar
Asitima
avatar
Joined: 23 May 2020
Last visit: 06 Oct 2023
Posts: 13
Own Kudos:
4
Given Kudos: 119
Location: India
Concentration: Nonprofit, Social Entrepreneurship
Schools: Fuqua '24 Haas '24 IESE '24 Erasmus Sloan '24 Tepper '24 Tuck '24 Wharton '24 Yale '24
GMAT 1: 620 Q47 V28
Schools: Fuqua '24 Haas '24 IESE '24 Erasmus Sloan '24 Tepper '24 Tuck '24 Wharton '24 Yale '24
GMAT 1: 620 Q47 V28
Posts: 13
Kudos: 4
What is the ratio of longest diagonal to the shortest diagonal in a re 04 Jun 2021, 10:18
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I find the easiest way to consider the octagon circumscribed in a circle. As it is a regular polygon, naturally, the longest distance inside the octagon is the longest length of the circle = diameter. From here it can be seen that longest diagonal and shortest diagonal form one leg and hypotenuse of an isosceles right triangle.

Ratio Sqrt 2 : 1
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 39,255
Own Kudos:
1,162
Posts: 39,255
Kudos: 1,162
What is the ratio of longest diagonal to the shortest diagonal in a re 18 Sep 2024, 06:40
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.
Moderator:
Bunuel
Math Expert
113752 posts