Question
The length of a rectangle is 8 cm less than the radius
of a circle. The perimeter of the rectangle is 60 cm, and the ratio of its length to breadth is 4:2. Find how much greater the area of the circle is than the area of the rectangle.Solution
ATQ, Let the length and breadth of the rectangle be 4a cm and 2a cm, respectively. Perimeter of the rectangle = 2 × (Length + Breadth) 60 = 2 × (4a + 2a) 60 = 2 × 6a 60 = 12a a = 5 Length of the rectangle = 4a = 4 × 5 = 20 cm Breadth of the rectangle = 2a = 2 × 5 = 10 cm Given length is 8 cm less than the radius, Radius of the circle = 20 + 8 = 28 cm Area of the circle = πr² = 22/7 × 28 × 28 = 2464 cm² Area of the rectangle = 20 × 10 = 200 cm² Required difference = 2464 − 200 = 2264 cm²
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