|
Author |
Message |
|
TAGS:
|
|
|
Manager
Joined: 06 Apr 2010
Posts: 149
Location: Pune
Schools: INSEAD, ISB, HKUST, HEC Paris, Warwick
WE 1: 2 yrs Credit Analyst
WE 2: 5 yrs Transition Manager
Followers: 3
Kudos [?]:
16
[0], given: 11
|
In the figure shown, two identical squares are inscribed in [#permalink]
 27 Aug 2010, 23:01
Question Stats:
79% (04:15) correct
20% (02:33) wrong based on 0 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? Attachment: 
Rectangle.png [ 19.46 KiB | Viewed 790 times ]
A. 8√2 B. 12 C. 12√2 D. 16 E. 18
Last edited by Bunuel on 18 Sep 2012, 00:54, edited 1 time in total.
Edited the question.
|
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 11610
Followers: 1800
Kudos [?]:
9593
[1] , given: 828
|
Re: Geometry-Square within Rectangle [#permalink]
28 Aug 2010, 07:45
1
This post received
KUDOS
|
|
|
|
|
|
Manager
Joined: 30 Sep 2009
Posts: 101
Followers: 0
Kudos [?]:
12
[1] , given: 66
|
Re: Geometry question [#permalink]
17 Sep 2012, 22:15
1
This post received
KUDOS
dineesha wrote: In the figure shown, two identical squares are inscribed in the rectangle. If the perimeter of the
rectangle is 18\sqrt{2}, then what is the perimeter of each square?
A. 8\sqrt{2}
B. 12
C. 12\sqrt{2}
D. 16
E. 18
Please see figure in the attached file. PERIMETER=2(A+B) WHERE A AND B ARE TWO SIDES OF THE RECTANGLE..... A --> THE LENGTH B-- > THE BREADTH AS THE TWO SQUARES ARE IDENTICAL THE DIAGONALS ARE EQUAL TO B . THEREFORE A=2B .. ON EQUATING WE WILL GET THE ANSWER
|
|
|
|
|
|
Intern
Joined: 24 Aug 2010
Posts: 5
Followers: 0
Kudos [?]:
2
[0], given: 0
|
Re: Geometry-Square within Rectangle [#permalink]
28 Aug 2010, 07:45
Hello  Let's name: A width of the rectangle (the biggest line) B height of the rectangle (the smallest line) C width of the square We know that 2 (A + B) = 18√2, so A + B = 9√2 We can also infer that A = 2B since A = 2 diagonal of the square and B = 1 diagonal of the square (see it on the figure to understand it more easily) A = 3√2 and B = 6√2 From Pythagor, we have C² + C² = B² <=> 2c² = (3√2)² <=> 2c² = 9 * 2 <=> C = 3 So the perimeter of each square is 4 * 3 = 12
|
|
|
|
|
|
Manager
Joined: 09 Jun 2010
Posts: 116
Followers: 2
Kudos [?]:
30
[0], given: 1
|
Re: Geometry-Square within Rectangle [#permalink]
28 Aug 2010, 07:49
let each square is with side a & diagonal b. hence a = 1/\sqrt{2}b. b is breadth of the bigger rectangle & 2b is the length of the rectangle. perimeter of the rectangle is 2X(2b+b) = 6b = 18\sqrt{2} b = 3\sqrt{2} => a = 3. perimeter of each square = 12. Answer is B
|
|
|
|
|
|
SVP
Joined: 16 Nov 2010
Posts: 1721
Location: United States (IN)
Concentration: Strategy, Technology
Followers: 26
Kudos [?]:
228
[0], given: 34
|
Re: Geometry-Square within Rectangle [#permalink]
19 Apr 2011, 18:09
l+b = 9root(2) (l - length of rectange, b - breadth of rectangle) Also, 2d + d = 9root(2) (d = Diagonal of square) d = 3root(2) Side of square = 3, so permieter = 4 * 3 = 12 Answer - B
_________________
Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
Intern
Joined: 07 Aug 2012
Posts: 28
Location: United States
Concentration: Finance, Strategy
GMAT 1: 710 Q50 V35
GPA: 3.7
WE: Consulting (Insurance)
Followers: 0
Kudos [?]:
5
[0], given: 3
|
In the figure shown, two identical squares are inscribed in the rectangle. If the perimeter of the rectangle is 18\sqrt{2}, then what is the perimeter of each square? A. 8\sqrt{2} B. 12 C. 12\sqrt{2} D. 16 E. 18 Please see figure in the attached file.
Attachments
temp.JPG [ 12.87 KiB | Viewed 820 times ]
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 11610
Followers: 1800
Kudos [?]:
9593
[0], given: 828
|
Re: Geometry question [#permalink]
18 Sep 2012, 00:56
|
|
|
|
|
|
Manager
Joined: 28 Feb 2012
Posts: 77
Concentration: Strategy, International Business
GPA: 3.9
WE: Marketing (Other)
Followers: 0
Kudos [?]:
8
[0], given: 9
|
Re: In the figure shown, two identical squares are inscribed in [#permalink]
26 Sep 2012, 01:40
Interesting questions and i like such questions. Since diagonal of the square is equal to side of the square*sqrt2 then we have one side of the reqtangle is equal to two diagonal of the square and another side of the rectangle is equal to one diagonal. All the sides (perimiter) are equal to 6 diagonals. So the side of the square is equal to 18\sqrt{2}/6\sqrt{2}=3. Then perimiter of the square 3*4=12
_________________
If you found my post useful and/or interesting - you are welcome to give kudos!
|
|
|
|
|
|
Senior Manager
Joined: 13 Aug 2012
Posts: 468
Followers: 12
Kudos [?]:
75
[0], given: 11
|
Re: In the figure shown, two identical squares are inscribed in [#permalink]
26 Sep 2012, 02:25
Answer is B. See Solution.
Attachments
solution mixture.jpg [ 31.89 KiB | Viewed 595 times ]
|
|
|
|
|
|
|
Re: In the figure shown, two identical squares are inscribed in
[#permalink]
26 Sep 2012, 02:25
|
|
|
|
|
|
|
|
|
|
|
close
