Question

The radius of the circumcircle of an equilateral triangle of side 12 cm is

• A. \((\frac{4}{3})\)\(\sqrt{3}\) cm
• B. 4\(\sqrt{3}\) cm
• C. 4\(\sqrt{2}\) cm
• D. \((\frac{4}{3})\)\(\sqrt{2}\) cm

Answer 1

The Correct Option is B

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