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In the figure shown, two identical squares are inscribed in [#permalink]
27 Aug 2010, 22:01

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Difficulty:

35% (medium)

Question Stats:

74% (03:10) correct
26% (02:49) wrong based on 85 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?

Re: Geometry-Square within Rectangle [#permalink]
28 Aug 2010, 06:45

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Expert's post

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.

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?

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 ..

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.

Merging similar topics. Please refer to the solutions above. _________________

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

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

Re: Geometry-Square within Rectangle [#permalink]
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.

Answer: B.

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

Re: Geometry-Square within Rectangle [#permalink]
03 Jan 2014, 06:31

Expert's post

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.

Answer: B.

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. _________________