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    Question

    Quantity I:   The total area of a Square and rectangle

    is 546 Sq cm. The side of the square is 14 cm. What is the sum of the perimeter of square and rectangle, if length of the rectangle is 25 cm? Quantity II:  The side of the equilateral triangle is equal to the diameter of the circle. The area of the equilateral triangle is 441√3 Sq cm. Find the circumference of the circle? 
    A Quantity I > Quantity II Correct Answer Incorrect Answer
    B Quantity I < Quantity II Correct Answer Incorrect Answer
    C Quantity I ≥ Quantity II Correct Answer Incorrect Answer
    D Quantity II ≥ Quantity I Correct Answer Incorrect Answer
    E Quantity I = Quantity II or Relation cannot be established Correct Answer Incorrect Answer

    Solution

    Quantity I:  a2 + lb = 546 142 + 25b = 546 196 + 25b = 546 25b = 546 – 196 25b = 350, b = 14 cm Perimeter of square = 4a = 4 `xx` 14 = 56 cm Perimeter of rectangle = 2 x (l + b) = 2 x (25 + 14) = 78 cm Required sum = 56 + 78 = 134 cm Quantity II:  The area of the equilateral triangle = 441√3 Sq cm The area of the equilateral triangle = (√3/4) `xx` a2  a2 = 441 `xx` 4 Side (a) = 21 `xx` 2 = 42 cm The diameter of the circle = 42 cm Radius (r) = 21 cm Circumference of the circle = 2πr = 2 x (22/7) x 21 = 132 cm 

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