A circle is inscribed in an equilateral triangle and a square is inscribed in the circle. The ratio of the area of the triangle to the area  of the square is

Let 'a'  be the side of an equilater at triangle, 'r'  be the radius of the circle, and 'x'  be the side     Of the square. Area of the equilateral triangle Δ=34a2  r=Δs=34a23a/2=a23. 2r=2x⇒x=2(a23)=a6  Area of the triangle: Area of the square =34a2:x2=34a2:a26=33:2