The radius of the circumcircle of an equilateral triangle of side 12 cm is
- \((\frac{4}{3})\)\(\sqrt{3}\) cm
- 4\(\sqrt{3}\) cm
- 4\(\sqrt{2}\) cm
- \((\frac{4}{3})\)\(\sqrt{2}\) cm
The Correct Option is B
Solution and Explanation
From the question we know that, Side of the equilateral triangle = 12 cm
Area of triangle = \(\frac{\sqrt{3}}{4} × Side^2\)
= \(\frac{\sqrt{3}}{4} × 12 × 12\) = \(36\sqrt{3} cm^2\)
Circumradius = \(R = \frac{abc}{4 × area of triangle}\)
= \(R = \frac{12 × 12 × 12}{4 × \sqrt{3}}\)
= \(R = \frac{12}{\sqrt{3}}\)
= \(4\sqrt{3} cm\)
The correct option is (B): 4\(\sqrt{3}\) cm
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