The perimeters of a circle, a square and an equilateral triangle are same and their areas are C, S and T respectively. Which of the following statement is true ?

Let the side of equilateral triangle be 'a' units

the radius of circle be 'r' units.

and the side of square be 'b' units

Then,

Perimeter of square = 4b

Perimeter of equilateral triangle = 3a

Circumference of circle = $$2*\pi*r$$

Then acc to ques,

=> $$4b = 3a = 2*\pi*r$$

=> b = $$\frac{\pi*r}{2}$$

=> a = $$\frac{2}{3} * \pi*r$$

Now,

area of circle (C) = $$\pi r^2$$

area of equilateral triangle (T) = $$\frac{\sqrt{3}}{4} * a^2$$

=> area of equilateral triangle (T) =$$\frac{\pi^2 * r^2}{3*\sqrt{3}}$$

area of square (S) = b*b

=> area of square (S) = $$\frac{\pi^2 r^2}{4}$$

Hence it is clearly visible that C > S > T.