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P 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 - Mathematics


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


  •  π :\[\sqrt{3}\]

  • 2 : \[\sqrt{\pi}\]

  •  3 :\[\pi\] 

  • \[\pi : \sqrt{2}\]

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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`

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RD Sharma Class 10 Maths
Chapter 13 Areas Related to Circles
Q 16 | Page 70
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