Question

Area of circle is equal to area of square then what is its perimeter ratio

Answer 1

let's take the radius of the circle and side of the square be r and a respectively. it is given area of the circle =area of the square=>
$\pi {r}^{2} = {a}^{2} => \pi = \frac{ {a}^{2} }{ {r}^{2} }$
=> √π= a/r=> 1\√π =r/a . Perimeter of the square= 4a and Perimeter of the circle=2πr Hence perimeter ratio of circle to square=2πr/4a=πr/2a=
π/2√π = √π/2 = 0.8866226925 approximately .
Hope it helps you....

Answer 2

Answer:

The ratio of their parameters will be √π : 2

Step-by-step explanation:

Let us consider the radius of a circle is 'r'

So the area of a circle is A = π*r²

and the parameter of the circle is 2*π*r

Let the sides of a square be x

So the area of the square is A = x*x = x²

and the parameter of square is 4*x

According to the given condition, the area of circle and area of the square is equal, so a relation generates;

π*r² = x²

Taking square root on both sides of the upper relation,

√π *r = x → (A)

Now taking ratio of their parameters,

2*π*r : 4*x

π*r : 2*x

Substituting the values of equation (A) implies;

π*r : 2*√π *r

√π : 2

Answer.