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02 Apr 2021, 21:18
Kudos
Bookmarks
Bunuel
Three identical circles are inscribed within an equilateral triangle, as shown above. If each of the radii of the circles is 3, what is the perimeter of the triangle?
A. 18(1+√3)
B. 9(1+2√3)
C. 18√3
D. 9(1+√3)
E. 6(1+√3)
See attached file:
Side of this equilateral triangle equals to 2r (middle part) + 2AB. Now, AB is a leg opposite 60 degrees in 30-60-90 right triangle. Sides in 30-60-90 right triangle are in the ration \(1:\sqrt{3}:2\), so \(AB=r\sqrt{3}\)
So you can see that: side equals to \(2r+2*(r\sqrt{3})=6+6\sqrt{3}\), so \(P=3*(6+6\sqrt{3})=18(1+\sqrt{3})\).
Answer: A.
A. 18(1+√3)
B. 9(1+2√3)
C. 18√3
D. 9(1+√3)
E. 6(1+√3)
See attached file:
Attachment:
Triangle.PNG
Side of this equilateral triangle equals to 2r (middle part) + 2AB. Now, AB is a leg opposite 60 degrees in 30-60-90 right triangle. Sides in 30-60-90 right triangle are in the ration \(1:\sqrt{3}:2\), so \(AB=r\sqrt{3}\)
So you can see that: side equals to \(2r+2*(r\sqrt{3})=6+6\sqrt{3}\), so \(P=3*(6+6\sqrt{3})=18(1+\sqrt{3})\).
Answer: A.
I am wondering here why 4 x (3√3) <--- side of one triangle wouldn't give us the same result.
30 Jan 2025, 01:10
Kudos
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Hello from the GMAT Club BumpBot!
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Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
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