Question
The length of a rectangle is 7 cm more than the radius
of a circle. The perimeter of the rectangle is 60 cm, and the ratio of its length to breadth is 7:3. Find the difference between the area of the circle and the area of the rectangle.Solution
ATQ, Let the length and breadth of the rectangle be 7a cm and 3a cm, respectively. According to the question, Perimeter of the rectangle = 2 × (Length + Breadth) 60 = 2 × (7a + 3a) 60 = 2 × 10a 60 = 20a a = 3 Length of the rectangle = 7a = 7 × 3 = 21 cm Breadth of the rectangle = 3a = 3 × 3 = 9 cm The radius of the circle = 21 − 7 = 14 cm Area of the circle = πr² = 22/7 × 14 × 14 = 616 cm² Area of the rectangle = 21 × 9 = 189 cm² Required difference = 616 − 189 = 427 cm²
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