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

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27 Aug 2010, 23:01

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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?

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.

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 [#permalink]

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30 Jul 2016, 06:07

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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

answer is B

Attachments

Rectangle.png [ 101.26 KiB | Viewed 7168 times ]

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

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02 Jul 2017, 05:35

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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

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

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

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21 Nov 2013, 14:45

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

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.

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.