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√ (c) π : 2 (d) √ : 2
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,
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√iπr [ a=r√ ]
Thus the ratio is 2√