Find all School-related info fast with the new School-Specific MBA Forum

It is currently 02 Sep 2014, 08:56

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

In the figure shown, two identical squares are inscribed in the rectan

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Senior Manager
Senior Manager
User avatar
Joined: 11 Sep 2005
Posts: 331
Followers: 1

Kudos [?]: 9 [0], given: 0

GMAT Tests User
In the figure shown, two identical squares are inscribed in the rectan [#permalink] New post 14 Oct 2007, 02:58
1
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 100% (00:00) wrong based on 1 sessions
In the figure shown, two identical squares are inscribed in the rectangle. If the perimeter of the rectangle is 18√2, then what is the perimeter of each square?
Image

A. 8√2
B. 12
C. 12√2
D. 16
E. 18

OPEN DISCUSSION OF THIS QUESTION IS HERE: in-the-figure-shown-two-identical-squares-are-inscribed-in-99925.html
[Reveal] Spoiler: OA

Attachments

set21-q8_Q.GIF
set21-q8_Q.GIF [ 2.02 KiB | Viewed 529 times ]


Last edited by Bunuel on 02 Sep 2014, 02:26, edited 1 time in total.
Edited the question and added the OA.
Kaplan GMAT Prep Discount CodesKnewton GMAT Discount CodesManhattan GMAT Discount Codes
Senior Manager
Senior Manager
User avatar
Joined: 11 Sep 2005
Posts: 331
Followers: 1

Kudos [?]: 9 [0], given: 0

GMAT Tests User
Re: In the figure shown, two identical squares are inscribed in the rectan [#permalink] New post 14 Oct 2007, 02:59
Sorry for the easy one...........but somthng wrong with given choice & OA, i suppose!
Director
Director
User avatar
Joined: 09 Aug 2006
Posts: 529
Followers: 2

Kudos [?]: 23 [0], given: 0

GMAT Tests User
Re: In the figure shown, two identical squares are inscribed in the rectan [#permalink] New post 14 Oct 2007, 08:34
singh_amit19 wrote:
Sorry for the easy one...........but somthng wrong with given choice & OA, i suppose!


I get 6. Here is how ;

Given : Perimeter of rectangle = 18 / sqrt (2) = 9.sqrt(2)
2 (l+b) = 9.sqrt(2)
(l+b) = [9.sqrt(2) ] / 2 ------------ (1)
Looking at the diag, the diagonal of squares are a good benchmark to determine the length and breadth of rectangle.

Hence, b = 2l
Putting this in 1, we get

(l + 2l) = [9.sqrt(2) ] / 2
3l = [9.sqrt(2) ] / 2
l = [3.sqrt(2) ] / 2

This length is the diagonal of the square.. Hence lenght of diag is
[3.sqrt(2) ] / 2

Length of diagonal = a^2 + a^2 = [3.sqrt(2) ] / 2 (where a is the side of square)

2a ^2 = { [3.sqrt(2) ] / 2 } ^2
a ^2 = 9/4
a = 3/2

Perimeter of a square = 4. a = 4 . 3/2 = 6.
Director
Director
User avatar
Joined: 30 Nov 2006
Posts: 592
Location: Kuwait
Followers: 11

Kudos [?]: 148 [0], given: 0

GMAT Tests User
Re: In the figure shown, two identical squares are inscribed in the rectan [#permalink] New post 15 Oct 2007, 06:15
If L = side of the square
then the diagonal of the square D = sqrt(2)*L
From the figure, the perimeter of the rectangle is 6 times the diagonal of the square.
[ You can see that the length is the sum of two diagonals and the width is also a diagonal of the square]

6D = 18*sqrt(2) = sqrt(2)*6L = 18 sqrt(2)
6L = 18 --> L = 3
The perimeter of the square is 4L = 12

ANSWER: B
Director
Director
User avatar
Joined: 03 May 2007
Posts: 899
Schools: University of Chicago, Wharton School
Followers: 6

Kudos [?]: 44 [0], given: 6

GMAT Tests User
Re: In the figure shown, two identical squares are inscribed in the rectan [#permalink] New post 15 Oct 2007, 07:07
Daignal of a square = d = 18 sqrt2/6 = 3 sqrt 2
d = (side of the square) (sqrt 2)
3 sqrt2 = (side) sqrt 2
side = 3

perimeter of each square = 3 x 4 = 12
Director
Director
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 842
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Followers: 5

Kudos [?]: 203 [0], given: 165

Re: In the figure shown, two identical squares are inscribed in the rectan [#permalink] New post 02 Sep 2014, 00:19
Refer diagram below:
Attachment:
set21-q8_Q.GIF
set21-q8_Q.GIF [ 3.47 KiB | Viewed 42 times ]


Perimeter of rectangle = \frac{18}{\sqrt{2}}

Lets say one side = x

other side = \frac{9}{\sqrt{2}} - x

When we divide the rectangle (as shown in fig), two squares would be formed

one side = x; other side = \frac{9}{2\sqrt{2}} - \frac{x}{2}

As square ABCD is formed, both sides should be equal

x = \frac{9}{2\sqrt{2}} - \frac{x}{2}

x = \frac{3}{\sqrt{2}}

Area of Square ABCD= \frac{3}{\sqrt{2}} * \frac{3}{\sqrt{2}} = \frac{9}{2}

Area of inscribed square PQRS = \frac{1}{2} * \frac{9}{2} = \frac{9}{4}

Length of a side of square PQRS = \sqrt{\frac{9}{4}} = \frac{3}{2}

Perimeter of square PQRS= \frac{3}{2} * 4 = 6

Bunuel, can you kindly update OA?
_________________

Kindly press "+1 Kudos" to appreciate :)

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 25253
Followers: 3430

Kudos [?]: 25267 [0], given: 2702

Re: In the figure shown, two identical squares are inscribed in the rectan [#permalink] New post 02 Sep 2014, 02:27
Expert's post
singh_amit19 wrote:
In the figure shown, two identical squares are inscribed in the rectangle. If the perimeter of the rectangle is 18√2, then what is the perimeter of each square?
Image

A. 8√2
B. 12
C. 12√2
D. 16
E. 18


The rectangle's width=d and length=2d, where d is the diagonal of each square.

P_{rectangle}=2(d+2d)=18\sqrt{2} --> d=3\sqrt{2}.

Now, d^2=s^2+s^2, where s is the side of a square --> d^2=(3\sqrt{2})^2=18=2s^2 --> s=3 --> P_{square}=4s=12.

Answer: B.

OPEN DISCUSSION OF THIS QUESTION IS HERE: in-the-figure-shown-two-identical-squares-are-inscribed-in-99925.html
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Re: In the figure shown, two identical squares are inscribed in the rectan   [#permalink] 02 Sep 2014, 02:27
    Similar topics Author Replies Last post
Similar
Topics:
Circle is inscribed in the square as shown in figure PareshGmat 1 01 Sep 2014, 19:46
8 Experts publish their posts in the topic In the figure shown, two identical squares are inscribed in udaymathapati 14 27 Aug 2010, 22:01
if two identical squares are inscribed in the rectangle. If Jcpenny 1 14 Oct 2008, 14:40
In the figure shown, two identical squares are inscribed in marcodonzelli 1 12 Jan 2008, 02:17
In the figure shown above, two identical squares are humtum0 2 09 Jun 2007, 18:52
Display posts from previous: Sort by

In the figure shown, two identical squares are inscribed in the rectan

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.