A wire is in the form of an equilateral triangle with an area of 36\sqrt{3} cm^2. If it is changed into a semicircle, then what is its radius?

Explanation

Area of the equilateral triangle = \frac{\sqrt{3}}{4}a^2 = 36\sqrt{3}, so a^2 = 144 and side a = 12 cm. The total length of the wire is 3 \times 12 = 36 cm. Perimeter of the semicircle is \pi r + 2r = 36, thus r = \frac{36}{\pi + 2}. This matches none of the given options.

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