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      Question

      The perimeter of a sector of a circle, whose radius is

      15 cm, is 61 cm. If the length of a rectangle is 10 cm more than the arc subtended by the sector and its perimeter is 90 cm, then find the area (in cm2) of the rectangle.
      A 124 Correct Answer Incorrect Answer
      B 144 Correct Answer Incorrect Answer
      C 164 Correct Answer Incorrect Answer
      D 145 Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      Let the arc subtended by the sector be ‘l’ cm and the radius of the circle be ‘r’ cm According to the question, (l + 2r) = 61 Or, l = 61 – 2r = 61 – (2 × 15) = 31 cm Therefore, length of the rectangle = 31 + 10 = 41 cm Let the breadth of the rectangle be ‘b’ cm Therefore, 2 × (41 + b) = 90 Or, b = 45 – 41 = 4 cm Therefore, area of the rectangle = length × breadth = 4 × 41 = 164 cm2

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