Question

If the area of a square is same as the area of a circle, then the ratio of their perimeters, in terms of π, is

Options

•  π :\[\sqrt{3}\]

• 2 : \[\sqrt{\pi}\]

•  3 :\[\pi\] 

• \[\pi : \sqrt{2}\]

Answer 1

We have given that area of a circle of radius r is equal to the area of a square of side a.

`∴ pir^2=a^2`

`∴ a=sqrtpir`

We have to find the ratio of the perimeters of circle and square. 

`∴ "perimeter of circle"/"Perimeter oof square"=(2pi r)/(4a)`    ..................(1)

Now we will substitute `a=sqrtpir` in equation (1)

`∴ "perimeter of circle"/"Perimeter oof square"=(2pi r)/(4sqrtr)` 

`∴ "perimeter of circle"/"Perimeter oof square"=pi/(2sqrtpi)`

`∴ "perimeter of circle"/"Perimeter oof square"=sqrtpi/2`

Therefore, ratio of their perimeters is `sqrtpi:2`