MCQ

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 :\[\pi\]

\[\pi : \sqrt{2}\]

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#### Solution

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`

Concept: Area of Circle

Is there an error in this question or solution?

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