Direction: Consider the following for the next two (02) items:An equilateral triangle ABC is inscribed in a circle of radius 20√3Q. What is the length of the side of the triangle?a)30 cmb)40 cmc)50 cmd)60 cmCorrect answer is option 'D'. Can you explain this answer?

Question

Direction: Consider the following for the next two (02) items:An equilateral triangle ABC is inscribed in a circle of radius 20&radic;3Q. What is the length of the side of the triangle?a)30 cmb)40 cmc)50 cmd)60 cmCorrect answer is option 'D'. Can you explain this answer?

Answer

Radius of circumcircle of an equilateral triangle = side / √3
R = a/√3
a = R√3 = 20√3 * √3 = 60cm

Answer

Explanation:
Prerequisites:
- The radius of a circle circumscribed around an equilateral triangle is given by the formula: R = a√3 / 3, where 'a' is the side length of the equilateral triangle.
- In this case, R = 20√3.

Calculation:
- Given R = 20√3, we can substitute this into the formula above:
20√3 = a√3 / 3
- Simplifying, we get:
a = 60 cm
Therefore, the length of the side of the equilateral triangle inscribed in the circle of radius 20√3 is 60 cm. So, the correct answer is option 'D'.

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