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?

• A. Only II
• B. Neither I nor II
• C. Only I
• D. Both I and II

Answer: (C)

Let the radius of circle is 'r' and a side of a square is 'a', then given condition2?r = 4a ? a = ?r/2? Area of square = (?r/2)2 = ?2 /4r2 = 9.86r2/4 = 2.46r2and area of circle = ?r2 = 3.14;r2and let the side of equilateral triangle is x.Then, given condition,3x = 2?r ? x = 2?r/3? Area of equilateral triangle = ?3/4 x 2= ?3/4 x 4?2r2/9= ?2/3?3r2= 1.89r2Hence, Area of circle > Area of square > Area of equilateral triangle.