What is the length of the side of the triangle ABC?
Consider the following for the next two (02) items that follow: Consider a circle of area 9 square unit and an equilateral triangle ABC as shown in the figure given below.
- A. 2\sqrt{3} unit
- B. 4\sqrt{3} unit
- C. 6\sqrt{3} unit ✓
- D. 8\sqrt{3} unit
Correct Answer: C. 6\sqrt{3} unit
Explanation
Interpreting the area of the inscribed circle as 9\pi (a common OCR omission of \pi), its radius is r=3. The radius of an incircle in an equilateral triangle is r = \frac{a}{2\sqrt{3}}. Substituting r=3 gives a = 3 \times 2\sqrt{3} = 6\sqrt{3} units.
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