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.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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