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gmat_thingie
- Junior | Next Rank: 30 Posts
- Posts: 23
- Joined: Thu Nov 12, 2009 12:37 am
In a 30-60-90 triangle, the sides are in the following ratio:
x : x√3 : 2x.
This ratio can also be represented as follows:
x/2 : (x/2)√3 : x.
An equilateral triangle that has an area of 9√3 is inscribed in a circle. What is the area of the circle?
A. 6Ï€
B. 9Ï€
C. 12Ï€
D. 9π√3
E. 18π√3
In the figure above:
AC = 2(AD) = 2(r/2)√3 = r√3.
BD = r + r/2 = 3r/2.
Since the area of ∆ABC is 9√3, we get:
(1/2)(AC)(BD) = 9√3
(1/2)(r√3)(3r/2) = 9√3
3r²/4 = 9
3r² = 36
r² = 12.
Thus:
Area of circle = πr² = 12π.
The correct answer is C.
