Question

if the perimeter of a circle is equal to that of a square, then find the ratio of their area

Answer 1

A.T.Q


2Pir = 4s

pir = 4s/2

pir=2s

pir/2=s

area of square = side^2
=pir/2×pir/2
=(pir)^2/4

area of circle = pir^2
= pir^2

ratio of there areas = (pir)^2/4/pir^2/1
= pi/4
= 22/7/4
=22/28
=11/14
=11:14

Hope it helps you friend .
Have a nice day.

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.