Question

If the area of a square is same as the area of a circle. find the ratio of the perimeter of the square and that of the circle
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Answer 1

Answer:

Ratio of Perimeter of square & perimeter of circle is 2 : √π .

2 : √π is the correct answer.

Step-by-step explanation:

Let ‘r’ be the radius of a circle and ‘a’ be the side of a square.

Given :  

Area of square = Area of circle

πr² = a²

a = √(π)r ………….(1)

Ratio of Perimeter of square & perimeter of circle

Perimeter of square,P1 :  Perimeter of circle , P2

P1: P2 = 4a :  2πr  

P1/ P2 =  4a  / 2πr

P1/ P2 = 4(√π r) / 2πr  

P1/ P2 = 2√π / π  

P1/ P2 = (2√π ×√π)/ (π × √π)  

[Multiply by √π in the denominator and numerator]

P1/ P2 = 2π/π√π

P1/ P2 = 2 / √π

P1: P2 = 2 :  √π  

Ratio of Perimeter of square & perimeter of circle = 2 : √π  

Hence, Ratio of Perimeter of square & perimeter of circle is 2 : √π .

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