Question

If the perimeter of a circle is equal to that of a square, then the ratio of their areas is​

Answer 1

Answer:

Given the perimeter of the circle is equal to that of the square.

P

circle

=P

square

Let r be the radius of the circle & a besides of square, then

2πr=4a

[

a

r

=

2π

4

=

π

2

]

Now

Areaofsquare

Areaofcircle

=

a

2

πr

2

=π(

a

r

)

2

Using

a

r

=

π

2

, we get

A

square

A

circle

=π(

π

2

)

2

=

π

2

4

×π=

π

4

Hence the ratio of Area of a circle to that of a square is

π

4

.

Answer 2

Step-by-step explanation:

perimeter of circle = circumference = 2πr

perimeter of square = 4a

2πr = 4a

πr = 2a

r = 2a/π

area of circle = πr²= π×4a²/π² =4a²/π

are of square = a²

so , ratio= 4a²/πa² = 4/π