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Three identical squares are perfectly inscribed within a rectangle as

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Three identical squares are perfectly inscribed within a rectangle as [#permalink]

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New post 01 Mar 2017, 01:56
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Question Stats:

84% (01:05) correct 16% (00:52) wrong based on 56 sessions

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Three identical squares are perfectly inscribed within a rectangle as shown above. If the perimeter of each square is 20, what is the area of the rectangle?

A. \(25\sqrt{2}\)

B. 50

C. \(75\sqrt{2}\)

D. 100

E. 150

Attachment:
SquaresInscribedRectangle2.png
SquaresInscribedRectangle2.png [ 5.36 KiB | Viewed 865 times ]

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Re: Three identical squares are perfectly inscribed within a rectangle as [#permalink]

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New post 01 Mar 2017, 02:07
Since the perimeter of the square is given,we can find the side of the square = 20/4=5
Now diagonal of square =5 * 2^1/2
If we connect the diagonals of the square we can find that they together become the length of the rectangle, so length of rect =3×5×2^1/2
Breadth =5×2^1/2
So area of rect = 150

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Three identical squares are perfectly inscribed within a rectangle as [#permalink]

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New post 01 Mar 2017, 02:45
3
Bunuel wrote:
Image
Three identical squares are perfectly inscribed within a rectangle as shown above. If the perimeter of each square is 20, what is the area of the rectangle?

A. \(25\sqrt{2}\)

B. 50

C. \(75\sqrt{2}\)

D. 100

E. 150

Attachment:
The attachment SquaresInscribedRectangle2.png is no longer available


Hence option E is correct
Hit Kudos if you liked it 8-)
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Untitled.png [ 14.31 KiB | Viewed 744 times ]

Three identical squares are perfectly inscribed within a rectangle as   [#permalink] 01 Mar 2017, 02:45
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