Question

The perimeter of a circle is equal to that of a square. Their areas are in the ratio of ____.

Answer 1

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Answer 2

Answer:

The ratio of their areas 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 b 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 parameter of circle and parameter of the square is equal, so a relation generates;

2*π*r = 4*x

π *r = 2*x

(π *r)/2 = x → (A)

Now taking ratio of their areas,

π*r² : x²

Taking square roots on both sides;

√π*r : x

Substituting the values of equation (A) implies;

√π*r : (π *r)/2

√π : 2

Answer.