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

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

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14 Oct 2007, 03:58
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Difficulty:

55% (hard)

Question Stats:

61% (01:51) correct 39% (02:21) wrong based on 128 sessions

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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?

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 [ 2.02 KiB | Viewed 2532 times ]

Last edited by Bunuel on 02 Sep 2014, 03:26, edited 1 time in total.
Edited the question and added the OA.

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

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14 Oct 2007, 03:59
Sorry for the easy one...........but somthng wrong with given choice & OA, i suppose!

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

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14 Oct 2007, 09:34
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.

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

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15 Oct 2007, 07:15
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

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

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15 Oct 2007, 08:07
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

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

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02 Sep 2014, 01:19
Refer diagram below:
Attachment:

set21-q8_Q.GIF [ 3.47 KiB | Viewed 2027 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?
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Re: In the figure shown, two identical squares are inscribed in the rectan [#permalink]

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02 Sep 2014, 03:27
Expert's post
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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?

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 --> $$d^2=(3\sqrt{2})^2=18=2s^2$$ --> $$s=3$$ --> $$P_{square}=4s=12$$.

OPEN DISCUSSION OF THIS QUESTION IS HERE: in-the-figure-shown-two-identical-squares-are-inscribed-in-99925.html
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Re: In the figure shown, two identical squares are inscribed in the rectan   [#permalink] 02 Sep 2014, 03:27
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