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  • Question
  • 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?


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

  • Correct Answer
  • Only I 

    Explanation

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

    ? Area of square = (?r/2)2 = ?2 /4r2 = 9.86r2/4 = 2.46r2
    and area of circle = ?r2 = 3.14;r2
    and 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
    = 1.89r2

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

  • Tags: Bank Exams

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