Question

The perimeter of a square is equal to the perimeter of a circle then ratio of thier area

Answer 1

The perimeter of a square is 4 * side.

Let the side be a.

==> Perimeter = 4a.........................(1)

Perimeter of a circle is the circumference :

Circumference = 2πr.............................(2)

where r is the radius

Since 1 and 2 are given equal

First equate 1 and 2:

==> 4 a = 2 π r

==> 2 a = π r

==>  a = π r / 2 .........................................(3)

Now area of square is a².........................(4)

Area of circle is πr²................................(5)

Now the ratio of the areas are:

See 4 and 5:

==> a² / π r²

But from 3 we know ==> a = π r / 2

So ratio:

===>  ( π r / 2 )² / π r²

===>  π ² r ² / 4 π r²

===>   π / 4

Thus the ratio of their areas is π / 4.

Hope it helps

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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.