Question
The length of sides of a square is twice the radius of a
circle and perimeter of a rectangle is half the perimeter of the square. If the sum of length and breadth of rectangle is 20 cm, then find the area of the circle (in cm2). [Take π = 2]Solution
Let the length of a square be ‘a’. And the radius of a circle be ‘r’. Now, a = 2r ----- (i) Perimeter of the rectangle = 1/2 × 4a = 2a => 2(l + b) = 2a => 2 × 20 = 2a => a = 20 cm Putting value of ‘a’ in (i) we get, Radius = r = 20/2 = 10 cm Area of the circle = πr2 = 2 × 10 × 10 = 200 cm2.
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