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      Question

      Perimeter of a rectangle is x cm and circumference of a

      circle is (x + 6) cm. The length of the rectangle is ______ cm. The ratio of the radius of the circle and the length of the rectangle is 1:2 and ratio of length and breadth of the rectangle is 7:3.
      A 35 cm Correct Answer Incorrect Answer
      B 21 cm Correct Answer Incorrect Answer
      C 25 cm Correct Answer Incorrect Answer
      D 15 cm Correct Answer Incorrect Answer
      E none of these Correct Answer Incorrect Answer

      Solution

      Let the length and breadth of the rectangle be 7a cm and 3a cm respectively. Perimeter of rectangle = 2 (7a + 3a) = 20a Radius of circle/Length of rectangle = 1/2 β‡’ r/7a = 1/2 According to the question β‡’ 2 Ο€ r – 20a = 6 β‡’ 2 x 22/7 x 7a/2 – 20a = 6 β‡’ 22a – 20a = 6 β‡’ 2a = 6 β‡’ a = 3 Β  Length of the rectangle = 7 x 3 = 21 cm

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