Question

Q6. It the perimeter of a circle is equal to that of a square then what
will be the ratio of their area​

Answer 1

1:1

Hope it is helpful for you

Answer 2

Answer: 4 : π or 14 : 11

Step-by-step explanation:

Let the radius of the circle be = r

Perimeter(Circumference) of the circle = 2πr

Let the side of the square be = s

Perimeter of the square = 4s

Perimeter of the circle = Perimeter of the square

2πr = 4s

2πr/4 = s

s = πr/2

Ratio of the area of the circle to the area of the square =

$\dfrac{Area \ of \ the \ circle}{Area \ of \ the \ square}$

$= \dfrac{\pi r^{2}}{s^{2}}$

$= \dfrac{\pi r^{2}}{(\dfrac{\pi r}{2})^{2}}$

$= \dfrac{\pi r^{2}}{\dfrac{\pi^2r^2}{4}}$

$= \dfrac{4\pi r^{2}}{\pi^2r^2}$

$= \dfrac{4}{\pi}$

∴ Ratio = 4 : π

If you take the value of pi as 22/7, then the ratio will be 14 : 11.

(4/π = 4/(22/7) = 28/22 = 14/11)