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

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Senior Manager
Joined: 11 Sep 2005
Posts: 331
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Kudos [?]: 7 [0], given: 0

In the figure shown, two identical squares are inscribed in [#permalink]  14 Oct 2007, 02:58
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In the figure shown, two identical squares are inscribed in the rectangle. If the perimeter of the rectangle is 18 by squareroot2, then what is the perimeter of each square?

(A)8 by squareroot2
(B)12
(C)12 by squareroot2
(D)16
(E)18
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Senior Manager
Joined: 11 Sep 2005
Posts: 331
Followers: 1

Kudos [?]: 7 [0], given: 0

Sorry for the easy one...........but somthng wrong with given choice & OA, i suppose!
Director
Joined: 09 Aug 2006
Posts: 529
Followers: 2

Kudos [?]: 23 [0], given: 0

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.
Director
Joined: 30 Nov 2006
Posts: 592
Location: Kuwait
Followers: 11

Kudos [?]: 145 [0], given: 0

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

Director
Joined: 03 May 2007
Posts: 899
Schools: University of Chicago, Wharton School
Followers: 6

Kudos [?]: 43 [0], given: 6

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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