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Three identical circles are drawn in a rectangle as shown above. If th

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Bunuel
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Three identical circles are drawn in a rectangle as shown above. If th [#permalink] New post   19 Jun 2020, 04:07
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Three identical circles are drawn in a rectangle as shown above. If the radius of each circle is 1, what is the area of the rectangle?


A. \(8+\sqrt{3}\)

B. \(8+2\sqrt{3}\)

C. \(8+3\sqrt{3}\)

D. \(8+4\sqrt{3}\)

E. \(8+5\sqrt{3}\)


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Re: Three identical circles are drawn in a rectangle as shown above. If th [#permalink] New post   19 Jun 2020, 04:29
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L =1+1+1+1 = 4

B = AD +1+1

\(AD = \sqrt{2^2-1^2}\) = √3

B =√3+2

L*B = 4*(√3+2) = 4√3+8
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Re: Three identical circles are drawn in a rectangle as shown above. If th [#permalink] New post   19 Jun 2020, 04:17
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Connect radius of circles,
Resulting an equilateral triangle of side 2
The height of equilateral triangle = (Side/2)*√3
Height = 2/2*√3
Height = √3
Height or breadth of rectangle= height of equilateral+2*radius.
=> 2+√3
Length of rectangle = 4*radius
=> 4*1 => 4

Area of rectangle = 4*(2+√3)
=> 8+4√3

Answer is D

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Re: Three identical circles are drawn in a rectangle as shown above. If th [#permalink] New post   19 Jun 2020, 04:46
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Option D

Let's denote the center of each circle as A, B, and C starting from top left and moving clockwise.
Draw a straight line passing through centers A and B. This is gives us the one side of the rectangle. which is nothing but 4 times the radius. lets call it S1= 4.

Notice that the centers A B and C form an equilateral triangle with side 2.
drop a perpendicular from C on line AB. Lets say it meets at point O

for the triangle AOC
AC = 2; AO=1 and OC = \(\sqrt{3}\) (using Pythagorean theorem)

using these we can find the other side on rectangle \(S2= \sqrt{3} + 1 + 1\)

S2 = 2+ \(\sqrt{3}\)

Area = S1*S2

\(4*(2+\sqrt{3})\)
\(8+4\sqrt{3}\)
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Re: Three identical circles are drawn in a rectangle as shown above. If th [#permalink] New post   20 Jun 2020, 11:45
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Kindly see the attachment.

width = b
The length is calculated in the right side.
D
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Re: Three identical circles are drawn in a rectangle as shown above. If th [#permalink] New post   22 Jan 2022, 13:22
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Re: Three identical circles are drawn in a rectangle as shown above. If th [#permalink]
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