It is currently 17 Dec 2017, 00:20

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

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

In the figure shown, two identical squares are inscribed in

Author Message
TAGS:

Hide Tags

Manager
Joined: 06 Apr 2010
Posts: 140

Kudos [?]: 974 [4], given: 15

In the figure shown, two identical squares are inscribed in [#permalink]

Show Tags

27 Aug 2010, 22:01
4
KUDOS
12
This post was
BOOKMARKED
00:00

Difficulty:

45% (medium)

Question Stats:

70% (01:36) correct 30% (02:01) wrong based on 410 sessions

HideShow timer Statistics

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 14546 times ]

A. 8√2
B. 12
C. 12√2
D. 16
E. 18
[Reveal] Spoiler: OA

Last edited by Bunuel on 17 Sep 2012, 23:54, edited 1 time in total.
Edited the question.

Kudos [?]: 974 [4], given: 15

Intern
Joined: 24 Aug 2010
Posts: 5

Kudos [?]: 5 [0], given: 0

Show Tags

28 Aug 2010, 06:45
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

Kudos [?]: 5 [0], given: 0

Math Expert
Joined: 02 Sep 2009
Posts: 42631

Kudos [?]: 135909 [10], given: 12715

Show Tags

28 Aug 2010, 06:45
10
KUDOS
Expert's post
2
This post was
BOOKMARKED
udaymathapati wrote:
In the figure attached (refer file), 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?
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 --> $$d^2=(3\sqrt{2})^2=18=2s^2$$ --> $$s=3$$ --> $$P_{square}=4s=12$$.

_________________

Kudos [?]: 135909 [10], given: 12715

Manager
Joined: 09 Jun 2010
Posts: 111

Kudos [?]: 152 [0], given: 1

Show Tags

28 Aug 2010, 06:49
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.

Attachments

Square within Rectangle.docx [17.79 KiB]

Kudos [?]: 152 [0], given: 1

TOEFL Forum Moderator
Joined: 16 Nov 2010
Posts: 1589

Kudos [?]: 607 [0], given: 40

Location: United States (IN)
Concentration: Strategy, Technology

Show Tags

19 Apr 2011, 17:09
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

_________________

Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

GMAT Club Premium Membership - big benefits and savings

Kudos [?]: 607 [0], given: 40

Manager
Joined: 30 Sep 2009
Posts: 115

Kudos [?]: 34 [2], given: 183

Show Tags

17 Sep 2012, 21:15
2
KUDOS
1
This post was
BOOKMARKED
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

AS THE TWO SQUARES ARE IDENTICAL THE DIAGONALS ARE EQUAL TO B . THEREFORE A=2B ..

ON EQUATING WE WILL GET THE ANSWER

Kudos [?]: 34 [2], given: 183

Manager
Joined: 28 Feb 2012
Posts: 115

Kudos [?]: 54 [0], given: 17

GPA: 3.9
WE: Marketing (Other)
Re: In the figure shown, two identical squares are inscribed in [#permalink]

Show Tags

26 Sep 2012, 00:40
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!

Kudos [?]: 54 [0], given: 17

Senior Manager
Joined: 13 Aug 2012
Posts: 457

Kudos [?]: 572 [2], given: 11

Concentration: Marketing, Finance
GPA: 3.23
Re: In the figure shown, two identical squares are inscribed in [#permalink]

Show Tags

26 Sep 2012, 01:25
2
KUDOS
1
This post was
BOOKMARKED
Attachments

solution mixture.jpg [ 31.89 KiB | Viewed 13702 times ]

_________________

Impossible is nothing to God.

Kudos [?]: 572 [2], given: 11

Current Student
Joined: 06 Sep 2013
Posts: 1965

Kudos [?]: 759 [0], given: 355

Concentration: Finance
Re: In the figure shown, two identical squares are inscribed in [#permalink]

Show Tags

21 Nov 2013, 13:45
udaymathapati 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?
Attachment:
Rectangle.png

A. 8√2
B. 12
C. 12√2
D. 16
E. 18

If y'all take a look you can tell that the length + width is equal to 3 diagonals of the square.
Therefore, Since 2(x+y) = 18 sqrt (2) then x+y = 9 sqrt (2)
Now as stated before we have 3s sqrt (2) = 9 sqrt (2)
s = 3, 's' stands for side of the square.
Perimeter = 12

Hope it helps
Kudos rain!
Cheers
J

Kudos [?]: 759 [0], given: 355

Manager
Joined: 13 Jul 2013
Posts: 69

Kudos [?]: 14 [0], given: 21

GMAT 1: 570 Q46 V24

Show Tags

03 Jan 2014, 06:23
Bunuel wrote:
udaymathapati wrote:
In the figure attached (refer file), 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?
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 --> $$d^2=(3\sqrt{2})^2=18=2s^2$$ --> $$s=3$$ --> $$P_{square}=4s=12$$.

Can I please ask why the width is D and length 2D?

Thank You

Kudos [?]: 14 [0], given: 21

Math Expert
Joined: 02 Sep 2009
Posts: 42631

Kudos [?]: 135909 [0], given: 12715

Show Tags

03 Jan 2014, 06:31
theGame001 wrote:
Bunuel wrote:
udaymathapati wrote:
In the figure attached (refer file), 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?
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 --> $$d^2=(3\sqrt{2})^2=18=2s^2$$ --> $$s=3$$ --> $$P_{square}=4s=12$$.

Can I please ask why the width is D and length 2D?

Thank You

The length is twice the width, so if $$width=d$$, then $$length=2d$$.
_________________

Kudos [?]: 135909 [0], given: 12715

Manager
Joined: 13 Jul 2013
Posts: 69

Kudos [?]: 14 [0], given: 21

GMAT 1: 570 Q46 V24

Show Tags

03 Jan 2014, 06:35
Bunuel wrote:

The length is twice the width, so if $$width=d$$, then $$length=2d$$.

This may sound a silly question but where is it stated that Length is twice the width? Is this a property of rectangle?

Kudos [?]: 14 [0], given: 21

Math Expert
Joined: 02 Sep 2009
Posts: 42631

Kudos [?]: 135909 [1], given: 12715

Show Tags

03 Jan 2014, 06:43
1
KUDOS
Expert's post
theGame001 wrote:
Bunuel wrote:

The length is twice the width, so if $$width=d$$, then $$length=2d$$.

This may sound a silly question but where is it stated that Length is twice the width? Is this a property of rectangle?

Not all rectangles have the ratio of width to length as 1 to 2.

From the figure we can see that the width equals to the diagonal of the inscribed square and the length equals to the two diagonals.
_________________

Kudos [?]: 135909 [1], given: 12715

SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1848

Kudos [?]: 2794 [0], given: 193

Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: In the figure shown, two identical squares are inscribed in [#permalink]

Show Tags

02 Sep 2014, 19:48
Perimeter of rectangle$$= 18\sqrt{2}$$

Lets say one side = x

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

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

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

As square ABCD is formed, both sides should be equal

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

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

Area of Square ABCD$$= 3\sqrt{2} * 3\sqrt{2} = 18$$

Area of inscribed square PQRS $$= \frac{1}{2} * 18 = 9$$ (This is a thumb rule/property for inscribed square)

Length of a side of square PQRS $$= \sqrt{9} = 3$$

Perimeter of square PQRS= 3 * 4 = 12

Attachments

Rectangle.png [ 29 KiB | Viewed 11851 times ]

_________________

Kindly press "+1 Kudos" to appreciate

Kudos [?]: 2794 [0], given: 193

Senior Manager
Status: Professional GMAT Tutor
Affiliations: AB, cum laude, Harvard University (Class of '02)
Joined: 10 Jul 2015
Posts: 448

Kudos [?]: 526 [0], given: 59

Location: United States (CA)
Age: 38
GMAT 1: 770 Q47 V48
GMAT 2: 730 Q44 V47
GMAT 3: 750 Q50 V42
GRE 1: 337 Q168 V169
WE: Education (Education)
Re: In the figure shown, two identical squares are inscribed in [#permalink]

Show Tags

12 Apr 2016, 19:55
Attached is a visual that should help.
Attachments

Screen Shot 2016-04-12 at 8.54.23 PM.png [ 131.08 KiB | Viewed 8438 times ]

_________________

Harvard grad and 770 GMAT scorer, offering high-quality private GMAT tutoring, both in-person and online via Skype, since 2002.

GMAT Action Plan - McElroy Tutoring

Kudos [?]: 526 [0], given: 59

Director
Joined: 04 Jun 2016
Posts: 645

Kudos [?]: 390 [2], given: 36

GMAT 1: 750 Q49 V43
In the figure shown, two identical squares are inscribed in [#permalink]

Show Tags

30 Jul 2016, 05:07
2
KUDOS
udaymathapati 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?
Attachment:
The attachment Rectangle.png is no longer available

A. 8√2
B. 12
C. 12√2
D. 16
E. 18

Given $$2l+2b=18√2$$
$$l+b=9√2$$ {equation 1}

As seen in the diagram that length of the RECTANGLE is diagonal + diagonal OF SQUARE ; length = $$2d$$
As seen in the diagram that breadth of the RECTANGLE is diagonal of the SQUARE =$$d$$
As seen in the diagram the side of the square is $$x$$

Substituting these values in equation 1 gives us
$$2d+d=9√2$$
$$3d=9√2$$
$$d=3√2$$ so the diagonal of the square is $$3√2$$
now $$side^2 + side^2 = diagonal ^2$$ {simple pythagorus theorum}
$$x^2+x^2= (3√2)^2$$

$$2x^2= 9*2=18$$

$$x^2=\frac{18}{2} = 9$$

$$x=\sqrt{9}$$

$$x= 3$$the side of the square is 3 therefore its perimeter is 3*4=12

Attachments

Rectangle.png [ 101.26 KiB | Viewed 7352 times ]

_________________

Posting an answer without an explanation is "GOD COMPLEX". The world doesn't need any more gods. Please explain you answers properly.
FINAL GOODBYE :- 17th SEPTEMBER 2016. .. 16 March 2017 - I am back but for all purposes please consider me semi-retired.

Kudos [?]: 390 [2], given: 36

Intern
Joined: 26 Jun 2015
Posts: 37

Kudos [?]: 3 [2], given: 25

Location: India
Concentration: Entrepreneurship, General Management
WE: Engineering (Energy and Utilities)
Re: In the figure shown, two identical squares are inscribed in [#permalink]

Show Tags

02 Jul 2017, 04:35
2
KUDOS
I solved it in a very easy way.
Lets take side of square is x. You can see from figure, two diagonals of squares = length of rectangle.
And one diagonal of square = width of rectangle.
So, as Length x Width = 36,
we can say (2 * root2x)* (root2x) = 36
x = 3
Perimeter of square = 12

Kudos [?]: 3 [2], given: 25

Re: In the figure shown, two identical squares are inscribed in   [#permalink] 02 Jul 2017, 04:35
Display posts from previous: Sort by