A square, a circle and equilateral triangle have same perimeter.Consider

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A square, a circle and equilateral triangle have same perimeter.
Consider the following statements.
I. The area of square is greater than the area of the triangle.
II. The area of circle is less then the area of triangle.
Which of the statement is/are correct ?

1. Only I
2. Only II
3. Both I and II
4. Neither I nor II

Correct Option: A

Let the radius of circle is 'r' and a side of a square is 'a',
then given condition
2πr = 4a
⇒ a = πr/2

∴ Area of square = (πr/2)² = π² /4r² = 9.86r²/4 = 2.46r²
and area of circle = πr² = 3.14;r²
and let the side of equilateral triangle is x.
Then, given condition,
3x = 2πr
⇒ x = 2πr/3

∴ Area of equilateral triangle = √3/4 x ²
= √3/4 x 4π²r²/9
= π²/3√3r²
= 1.89r²

Hence, Area of circle > Area of square > Area of equilateral triangle.