Last visit was: 25 Apr 2026, 10:31 It is currently 25 Apr 2026, 10:31
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
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 25 Apr 2026
Posts: 109,828
Own Kudos:
Given Kudos: 105,883
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,828
Kudos: 811,232
 [10]
1
Kudos
Add Kudos
9
Bookmarks
Bookmark this Post
User avatar
ArunSharma12
Joined: 25 Oct 2015
Last visit: 20 Jul 2022
Posts: 512
Own Kudos:
1,037
 [3]
Given Kudos: 74
Location: India
GMAT 1: 650 Q48 V31
GMAT 2: 720 Q49 V38 (Online)
GPA: 4
Products:
GMAT 2: 720 Q49 V38 (Online)
Posts: 512
Kudos: 1,037
 [3]
3
Kudos
Add Kudos
Bookmarks
Bookmark this Post
User avatar
freedom128
Joined: 30 Sep 2017
Last visit: 01 Oct 2020
Posts: 939
Own Kudos:
1,377
 [3]
Given Kudos: 402
GMAT 1: 720 Q49 V40
GPA: 3.8
Products:
GMAT 1: 720 Q49 V40
Posts: 939
Kudos: 1,377
 [3]
3
Kudos
Add Kudos
Bookmarks
Bookmark this Post
avatar
ConquerorGmat
Joined: 06 Apr 2020
Last visit: 01 Aug 2021
Posts: 5
Own Kudos:
6
 [1]
Given Kudos: 35
Posts: 5
Kudos: 6
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Answer-C
Use tan60 to get side of triangle if you are assuming square side to be X.
So side of equi. triangle is
X + 2*x/tan60.
Now ratio of area=area of square (side x)/area of triangle (X+2*X/tan60).after calculation and rationalisation..we will get Ans.c.

Posted from my mobile device
User avatar
lacktutor
Joined: 25 Jul 2018
Last visit: 23 Oct 2023
Posts: 658
Own Kudos:
1,447
 [1]
Given Kudos: 69
Posts: 658
Kudos: 1,447
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
∆ ABC is an equilateral triangle
Let (x+y) be the side of the triangle.
Let x be the side of the square.

∆ ABC and ∆ DBE are the similar triangles.
--> ∆ DBE an equilateral triangle too. (x is the side of that triangle)

Well, ∆ BHE and ∆ EFC are right-angled triangles and they are similar:

\(\frac{EF}{BH}= \frac{EC}{BE}\)

---> \(\frac{x}{(√3/2)x}= \frac{y}{x}\)

\(\frac{y}{x} =\frac{2}{√3}\)
--> \(BC=x+y = x+ (\frac{2}{√3})x= x( \frac{2+√3}{√3})\)

So, The ratio of the area of the square to that of the triangle is
\(\frac{x^{2}}{ (√3/4)(y^{2})}= \frac{x^{2}}{ (√3/4)(x^{2}(2+√3)^{2}/(√3)^{2}}= \frac{4√3}{(2+√3)^{2}}= \frac{4√3}{(7+4√3)}= \frac{12}{ 12+7√3}\)

Answer (C).

PLEASE SEE THE ATTACHED FILE.
Attachments

Geometry.png
Geometry.png [ 14.89 KiB | Viewed 24305 times ]

User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,985
Own Kudos:
Posts: 38,985
Kudos: 1,117
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:
Math Expert
109828 posts
Tuck School Moderator
852 posts