area and circumference of circle, triangle square

[ag]

Came across this question.

The length of the circumference of a circle equals the perimeter of a triangle of equal sides and also the perimeter of a square. The areas covered by the circle, triangle and square are c, t and s respectively. What can be said about the relation between c, t and s

1. s > t > c
2. c > t > s
3. c > s > t
4. s > c > t

is there a way to solve it without actually taking a value for the circumference?

[2iim]

You can verify the answer using numerical examples.

However, please note that what is given is a mathematical axiom

For a given circumference or perimeter, an equilateral triangle will be the regular polygon with the smallest area and a circle will the figure with the largest area.

A square with 4 sides having the same perimeter as that of an equilateral triangle will have an area larger than the equilateral triangle. Similarly, a regular pentagon's area will be larger than that of a square for the same perimeter and so on and so forth.

The answer to the question is option (3). i.e., C > S > T