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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) 2π (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=rπ

a=rπ

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=2rpiπr [ a=rπ ]

Thus the ratio is 2π


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