(b) 9 : 4√3.
Let each side of the square = a cm. Then,
Area of square = a2 cm2
Also, let r be the radius of the circle. Then, πr2 = a2
Let each side of the equilateral triangle = b cm.
Then 3b = 4a ⇒ b = \(\frac{4a}{3}\).
∴ Area of equilateral triangle = \(\frac{\sqrt3}{4}b^2\) = \(\frac{\sqrt3}{4}\)x \(\bigg(\frac{4a}{3}\bigg)^2\)
= \(\frac{\sqrt3}{4}\) x \(\frac{16a}{9}\) = \(\frac{4\sqrt3a^2}{9}\)
∴ Required ratio between area of circle and area of equilateral Δ is a2 : \(\frac{4\sqrt3a^2}{9}\) = 9 : 4√3.