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

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Joined: 02 Sep 2009
Posts: 50000
In the figure above, A and B are the centers of the two circles. If ea  [#permalink]

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14 Nov 2017, 23:44
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Difficulty:

35% (medium)

Question Stats:

83% (01:46) correct 17% (01:49) wrong based on 32 sessions

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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

Attachment:

2017-11-15_1036_001.png [ 6.79 KiB | Viewed 564 times ]

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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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15 Nov 2017, 00:57
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

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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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15 Nov 2017, 01:50
Bunuel wrote:

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

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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In the figure above, A and B are the centers of the two circles. If ea &nbs [#permalink] 15 Nov 2017, 01:50
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