Question : The circumference of a circle is equal to the perimeter of an equilateral triangle. If the radius of the circle is 7 cm, what is the length of the side of the equilateral triangle?
Option 1: $\frac{22}{3}$ cm
Option 2: $\frac{44}{3}$ cm
Option 3: $44$ cm
Option 4: $22$ cm
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Correct Answer: $\frac{44}{3}$ cm
Solution : The radius of the circle ($r$) = 7 cm Let 'a' be the side of an equilateral triangle. The circumference of a circle is equal to the perimeter of an equilateral triangle. $2 \pi r$ = 3a ⇒ a = $\frac{2 \pi r}{3}$ = $\frac{2 × 22 × 7}{7 × 3}$ = $\frac{44}{3}$ cm The side of the equilateral triangle is $\frac{44}{3}$ cm. Hence, the correct answer is $\frac{44}{3}$ cm.
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