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In the figure above, A and B are the centers of the two circles. If ea

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In the figure above, A and B are the centers of the two circles. If ea [#permalink]

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New post 14 Nov 2017, 22:44
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In the figure above, A and B are the centers of the two circles. If each circle has area 10, what is the area of the rectangle?

(A) 20
(B) 20 – 10/π
(C) 40/π
(D) 50/π
(E) 60/π


[Reveal] Spoiler:
Attachment:
2017-11-15_1036_001.png
2017-11-15_1036_001.png [ 6.79 KiB | Viewed 250 times ]
[Reveal] Spoiler: OA

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Kudos [?]: 135655 [0], given: 12705

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Re: In the figure above, A and B are the centers of the two circles. If ea [#permalink]

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New post 14 Nov 2017, 23:57
Let "a" and "b" be the sides of rectangle.
Since both circles have the same area, they have the same radius.
10=Pr^2
r=10^1/2 / P^1/2
It's obvius from teh picture above that "a"= 3*r/P^1/2 and "b"=2*r/P^1/2
Substituting we get
a=3*10^1/2/P^1/2 b= 2*10^1/2/P^1/2
Area of rectangle = a*b=2*3*10/P=60/P

Answer E

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In the figure above, A and B are the centers of the two circles. If ea [#permalink]

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New post 15 Nov 2017, 00:50
Bunuel wrote:
Image
In the figure above, A and B are the centers of the two circles. If each circle has area 10, what is the area of the rectangle?

(A) 20
(B) 20 – 10/π
(C) 40/π
(D) 50/π
(E) 60/π

[Reveal] Spoiler:
Attachment:
2017-11-15_1036_001.png


Since the area of the circle is 10,

π*r^2 = 10
r = \(\sqrt{10/π}\)
The breadth of the rectangle is the diameter of either circle which is \(2\sqrt{10/π}\)

Similarly, the length of the rectangle will be equal to \(3\sqrt{10/π}\)

Hence, the area of the rectangle will be \((2\sqrt{10/π})\)*\((3\sqrt{10/π})\) = 60/π(Option E)
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Kudos [?]: 750 [0], given: 20

In the figure above, A and B are the centers of the two circles. If ea   [#permalink] 15 Nov 2017, 00:50
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