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# Three identical squares are inscribed within a rectangle as shown abov

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Math Expert
Joined: 02 Sep 2009
Posts: 49932
Three identical squares are inscribed within a rectangle as shown abov  [#permalink]

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01 Mar 2017, 05:33
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Difficulty:

25% (medium)

Question Stats:

78% (01:58) correct 22% (02:00) wrong based on 72 sessions

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Three identical squares are inscribed within a rectangle as shown above. If the area of the rectangle is 216, what is the area of one of the squares?

A. 36

B. $$36\sqrt{2}$$

C. 54

D. $$54\sqrt{2}$$

E. 72

Attachment:

InscribedSquares3.png [ 6.55 KiB | Viewed 988 times ]

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

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01 Mar 2017, 08:45
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Bunuel wrote:

Three identical squares are inscribed within a rectangle as shown above. If the area of the rectangle is 216, what is the area of one of the squares?

A. 36

B. $$36\sqrt{2}$$

C. 54

D. $$54\sqrt{2}$$

E. 72

Attachment:
The attachment InscribedSquares3.png is no longer available

Let side of square =a

Length of rectangle = 3* diagonal of square (as 3 squares is there) = 3*a √2
Breadth of square = diagonal of square =a √2

given Length * breadth = 216
substituting above considered diagonal values

3*a √2 * a √2 =216
a^2 =216/6 =36 unit^2

Ans A
Attachments

InscribedSquares3.png [ 7.14 KiB | Viewed 846 times ]

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

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01 Mar 2017, 08:52
Let the side of the squares be a.

Width of the rectangle = length of diagonal of square = $$\sqrt{2}a$$
Length of rectangle = sum of diagonals of all 3 squares = $$3*\sqrt{2}a$$

Area of rectangle = ($$\sqrt{2}a$$)*($$3*\sqrt{2}a$$) = 6$$a^2$$

Hence 6$$a^2$$=216 =>$$a^2$$ = 36

Since side of square is a, the area of the square = $$a^2$$=36

Re: Three identical squares are inscribed within a rectangle as shown abov &nbs [#permalink] 01 Mar 2017, 08:52
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