Question

# The area of a circle is the same as the area of a square. Their perimeters are in the ratio. (a) 1 : 1 (b) 2√π (c) π : 2 (d) √π : 2

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Solution

## Given that areas of circle and square are equal. If a is the side of a square, then the area of the square is a2 units If r is the radius of a circle, then the area of the circle is πr2 units Thus, from the given condition, a2=πr2 →a=r√π →a=r√π The perimeter of a square is 4a The perimeter of a circle is 2π×r Thus the ratio of the perimeter of a square and a circle is 4a2πr=2r√piπr [ a=r√π ] Thus the ratio is 2√π

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