GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 03 Aug 2020, 13:24

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

Three identical circles are drawn in a rectangle as shown above. If th

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 65764
Three identical circles are drawn in a rectangle as shown above. If th  [#permalink]

Show Tags

New post 19 Jun 2020, 03:07
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

88% (01:59) correct 13% (04:09) wrong based on 24 sessions

HideShow timer Statistics

Image
Three identical circles are drawn in a rectangle as shown above. If the radius of each circle is 1, what is the area of the rectangle?


A. \(8+\sqrt{3}\)

B. \(8+2\sqrt{3}\)

C. \(8+3\sqrt{3}\)

D. \(8+4\sqrt{3}\)

E. \(8+5\sqrt{3}\)


Project PS Butler


Subscribe to get Daily Email - Click Here | Subscribe via RSS - RSS


Are You Up For the Challenge: 700 Level Questions

Attachment:
2020-06-19_1504.png
2020-06-19_1504.png [ 20.12 KiB | Viewed 417 times ]

_________________
PS Forum Moderator
User avatar
P
Joined: 18 Jan 2020
Posts: 1501
Location: India
GPA: 4
Premium Member CAT Tests
Re: Three identical circles are drawn in a rectangle as shown above. If th  [#permalink]

Show Tags

New post 19 Jun 2020, 03:17
2
Connect radius of circles,
Resulting an equilateral triangle of side 2
The height of equilateral triangle = (Side/2)*√3
Height = 2/2*√3
Height = √3
Height or breadth of rectangle= height of equilateral+2*radius.
=> 2+√3
Length of rectangle = 4*radius
=> 4*1 => 4

Area of rectangle = 4*(2+√3)
=> 8+4√3

Answer is D

Posted from my mobile device
DS Forum Moderator
User avatar
V
Joined: 19 Oct 2018
Posts: 2049
Location: India
Premium Member
Re: Three identical circles are drawn in a rectangle as shown above. If th  [#permalink]

Show Tags

New post 19 Jun 2020, 03:29
3
Attachment:
2020-06-19_1504.png
2020-06-19_1504.png [ 21.34 KiB | Viewed 357 times ]

L =1+1+1+1 = 4

B = AD +1+1

\(AD = \sqrt{2^2-1^2}\) = √3

B =√3+2

L*B = 4*(√3+2) = 4√3+8
Manager
Manager
User avatar
S
Joined: 04 Mar 2020
Posts: 75
Re: Three identical circles are drawn in a rectangle as shown above. If th  [#permalink]

Show Tags

New post 19 Jun 2020, 03:46
1
Option D

Let's denote the center of each circle as A, B, and C starting from top left and moving clockwise.
Draw a straight line passing through centers A and B. This is gives us the one side of the rectangle. which is nothing but 4 times the radius. lets call it S1= 4.

Notice that the centers A B and C form an equilateral triangle with side 2.
drop a perpendicular from C on line AB. Lets say it meets at point O

for the triangle AOC
AC = 2; AO=1 and OC = \(\sqrt{3}\) (using Pythagorean theorem)

using these we can find the other side on rectangle \(S2= \sqrt{3} + 1 + 1\)

S2 = 2+ \(\sqrt{3}\)

Area = S1*S2

\(4*(2+\sqrt{3})\)
\(8+4\sqrt{3}\)
Senior Manager
Senior Manager
User avatar
G
Joined: 05 Aug 2019
Posts: 330
Location: India
Concentration: Leadership, Technology
GMAT 1: 600 Q50 V22
GMAT 2: 670 Q50 V28 (Online)
GPA: 4
Re: Three identical circles are drawn in a rectangle as shown above. If th  [#permalink]

Show Tags

New post 20 Jun 2020, 10:45
1
Kindly see the attachment.

width = b
The length is calculated in the right side.
D
Attachments

1.jpeg
1.jpeg [ 51.62 KiB | Viewed 254 times ]

GMAT Club Bot
Re: Three identical circles are drawn in a rectangle as shown above. If th   [#permalink] 20 Jun 2020, 10:45

Three identical circles are drawn in a rectangle as shown above. If th

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne