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# Three identical squares are perfectly inscribed within a rectangle as

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Math Expert
Joined: 02 Sep 2009
Posts: 43851
Three identical squares are perfectly inscribed within a rectangle as [#permalink]

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01 Mar 2017, 00:56
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Difficulty:

25% (medium)

Question Stats:

83% (01:09) correct 17% (00:52) wrong based on 52 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

[Reveal] Spoiler:
Attachment:

SquaresInscribedRectangle2.png [ 5.36 KiB | Viewed 740 times ]
[Reveal] Spoiler: OA

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Joined: 09 Dec 2016
Posts: 6
Re: Three identical squares are perfectly inscribed within a rectangle as [#permalink]

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01 Mar 2017, 01:07
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
So area of rect = 150

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

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01 Mar 2017, 01:45
3
KUDOS
Bunuel wrote:

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

[Reveal] Spoiler:
Attachment:
The attachment SquaresInscribedRectangle2.png is no longer available

Hence option E is correct
Hit Kudos if you liked it
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Three identical squares are perfectly inscribed within a rectangle as   [#permalink] 01 Mar 2017, 01:45
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