# 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

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 :$\pi$

• $\pi : \sqrt{2}$

#### 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

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#### APPEARS IN

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