Question

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

Answer 1

Answer:

The required ratio is 4 : π

Step-by-step explanation:

Given :

The perimeter of a circle is equal to that of a square.

To find :

the ratio of their areas

Solution :

Let 'r' be the radius of the circle and 'a' be the side of the square.

Perimeter of the circle = 2πr

Perimeter of the square = 4a

Perimeter of the circle = Perimeter of the square

2πr = 4a

πr = 4a/2

πr = 2a

a = πr/2

Area of the circle/area of the square :

$= \dfrac{\pi r^2}{a^2} \\ = \dfrac{\pi r^2}{ \bigg(\dfrac{\pi r}{2} \bigg)^2} \\ = \dfrac{\pi r^2}{\dfrac{\pi ^2 r^2}{4}} \\ = \dfrac{1 \times 4}{\pi} \\ = \dfrac{4}{\pi}$

The ratio of their areas is 4 : π

Answer 2

Step-by-step explanation:

Let 'r' be the radius of the circle and 'a' be the side of the square.

Perimeter of the circle = 2πr

Perimeter of the square = 4a

Perimeter of the circle = Perimeter of the square

2πr = 4a

πr = 4a/2

πr = 2a

a = πr/2

Area of the circle/area of the square :

= π r²/a²

= πr²/(πr/2)²

= πr²/(π²r²/4)

= 1*4/π

{ 4/π }

The ratio of their areas is 4 : π

hopefully it will work ☺️☺️