Discussion

Explanation:

Perimeter of the equilateral triangle = P

∴ Side of the equilateral triangle = P/3

∴ The area of the equilateral triangle = $\frac{\sqrt{3}}{4}\times {\left(\frac{P}{3}\right)}^2$

But the area of the equilateral triangle is equal to the area of the circle.

Area of the circle = πr² = $\frac{\sqrt{3}}{4}\times {\left(\frac{P}{3}\right)}^2$

∴ Radius of the circle, r = $\sqrt{\left(\frac{\sqrt{3}}{\pi }\right)}\times \frac{P}{6}$

∴ The circumference of the circle = 2πr = $\frac{\sqrt{\left(\pi \sqrt{3}\right)}}{3}P$

Hence, option (d).

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