Question

what is the ratio of the areas of a circle and an equilateral triangle whose diameter and a side are respectively equal

Answer 1

the process is as follows---
diameter(d)=side of a triangle(a)
=>2r =a
=>r=a/2----->(***)
now,area of circle=2πr,where r is the radius.
=πa2/4[from (***)
area of eq.triangle=√3a2/4.
so area of eq.triangle to circle is=√3a2/4/πa2/4
=√3/π
the answer is √3:π......
hope u can understand a little.