The ratio of the area of a circle and that of an equilateral triangle, where the diameter of the circle is equal to the sides of the equilateral triangle, is:

Correct option is B

Given:

The diameter of the circle is equal to the side of the equilateral triangle.

Formula Used:

Area of the circle = $$= \pi r^2$$​​

​​where r is the radius of the circle.

Area of the equilateral triangle= $$= \frac{\sqrt{3}}{4} s^2$$​​

​​​where s is the side of the equilateral triangle.

Since the diameter of the circle is equal to the side of the equilateral triangle, we have:

s = 2r

Solution:

​$$\text{Ratio} = \frac{\pi r^2}{\frac{\sqrt{3}}{4} s^2}$$​​

Since s = 2r, we substitute $$s^2 = (2r)^2 = 4r^2:$$​​

Ratio = $$\frac{\pi r^2}{\frac{\sqrt{3}}{4} \times 4r^2} = \frac{\pi r^2}{\sqrt{3} r^2}$$​

Ratio $$= \frac{\pi}{\sqrt{3}}$$​