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      Question

      The length of a rectangle is 2 cm more than the radius

      of a circle. The perimeter of the rectangle is 108 cm, and the ratio of its length to breadth is 5:4. Find the difference between the area of the circle and the area of the rectangle.
      A 2264 cm² Correct Answer Incorrect Answer
      B 1952 cm² Correct Answer Incorrect Answer
      C 1744 cm² Correct Answer Incorrect Answer
      D 2465 cm² Correct Answer Incorrect Answer

      Solution

      ATQ, Let the length and breadth of the rectangle be 5a cm and 4a cm, respectively. Perimeter of the rectangle = 2 × (Length + Breadth) 108 = 2 × (5a + 4a) 108 = 2 × 9a 108 = 18a a = 6 Length of the rectangle = 5a = 5 × 6 = 30 cm Breadth of the rectangle = 4a = 4 × 6 = 24 cm The radius of the circle = 30 − 2 = 28 cm Area of the circle = πr² = 22/7 × 28 × 28 = 2464 cm² Area of the rectangle = 30 × 24 = 720 cm² Required difference = 2464 − 720 = 1744 cm²

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