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Six congruent circles are packed into an equilateral triangle so that

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Six congruent circles are packed into an equilateral triangle so that [#permalink]

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New post 08 Mar 2018, 21:17
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Six congruent circles are packed into an equilateral triangle so that no circle is overlapping and such that circles are tangent to one another or the triangle at any point of contact, as shown above. What is the area of the part of the triangle that is NOT covered by circles?

(1) The radius of each circle is 2
(2) The area of the triangle is \(48+28\sqrt{3}\)


Attachment:
six_circles_packed_1.png
six_circles_packed_1.png [ 16.87 KiB | Viewed 920 times ]

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Re: Six congruent circles are packed into an equilateral triangle so that [#permalink]

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New post 08 Mar 2018, 21:22
Bunuel wrote:
Image

Six congruent circles are packed into an equilateral triangle so that no circle is overlapping and such that circles are tangent to one another or the triangle at any point of contact, as shown above. What is the area of the part of the triangle that is NOT covered by circles?

(1) The radius of each circle is 2
(2) The area of the triangle is \(48+28\sqrt{3}\)


Attachment:
six_circles_packed_1.png


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Six congruent circles are packed into an equilateral triangle so that [#permalink]

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New post 09 Mar 2018, 01:07
Bunuel wrote:
Image

Six congruent circles are packed into an equilateral triangle so that no circle is overlapping and such that circles are tangent to one another or the triangle at any point of contact, as shown above. What is the area of the part of the triangle that is NOT covered by circles?

(1) The radius of each circle is 2
(2) The area of the triangle is \(48+28\sqrt{3}\)


Attachment:
The attachment six_circles_packed_1.png is no longer available


Question: Area of uncovered part of triangle = Area of triangle - Area of six circles = ?

Statement 1: The radius of each circle is 2
Using this information the side of the equilateral triangle can be calculated (using 30-60-90 property) as mentioned in attachment, Hence
SUFFICIENT

Statement 2: he area of the triangle is \(48+28\sqrt{3}\)
sing this information the side of the equilateral triangle can be calculated as mentioned in attachment, Hence
SUFFICIENT

Answer: option D
Attachments

File comment: www.GMATinsight.com
Screen Shot 2018-03-09 at 1.40.56 PM.png
Screen Shot 2018-03-09 at 1.40.56 PM.png [ 204.67 KiB | Viewed 608 times ]


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Re: Six congruent circles are packed into an equilateral triangle so that [#permalink]

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New post 10 Mar 2018, 20:42
1
There is a simpler approach to it, by trying to draw it on paper.
see the Sketch attached.

GMATinsight wrote:
Bunuel wrote:
Image

Six congruent circles are packed into an equilateral triangle so that no circle is overlapping and such that circles are tangent to one another or the triangle at any point of contact, as shown above. What is the area of the part of the triangle that is NOT covered by circles?

(1) The radius of each circle is 2
(2) The area of the triangle is \(48+28\sqrt{3}\)


Attachment:
The attachment six_circles_packed_1.png is no longer available


Question: Area of uncovered part of triangle = Area of triangle - Area of six circles = ?

Statement 1: The radius of each circle is 2
Using this information the side of the equilateral triangle can be calculated (using 30-60-90 property) as mentioned in attachment, Hence
SUFFICIENT

Statement 2: he area of the triangle is \(48+28\sqrt{3}\)
sing this information the side of the equilateral triangle can be calculated as mentioned in attachment, Hence
SUFFICIENT

Answer: option D

Attachments

WhatsApp Image 2018-03-11 at 09.09.28.jpeg
WhatsApp Image 2018-03-11 at 09.09.28.jpeg [ 99.73 KiB | Viewed 519 times ]


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Re: Six congruent circles are packed into an equilateral triangle so that   [#permalink] 10 Mar 2018, 20:42
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