The perimeter of an equilateral triangle is equal to circumference of…

Perimeter of equilateral triangle = 3a

ATQ,

⇒ 3a = circumference of circle

⇒ 3a = 2\(\pi\)r

⇒ a : r = 2\(\pi\) : 3

Area of circle = \(\pi r^2\)

Area of equilateral triangle = \(\frac{\sqrt {3}}{4} a^2\)

Required ratio = \(\frac{\sqrt {3}}{4} a^2\)  :  \(\pi r^2\)

                       =  \(\frac{\sqrt {3}}{4}\) (2\(\pi\))² : \(\pi\) 3²

                       =  \(\pi\) : 3\(\sqrt {3}\)

                       = 22 : 21\(\sqrt {3}\)