Question

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

Answer 1

Answer:

14:11 is the ratio of their areas.

Answer 2

Let the radius of the circle =r.

∴ Its circumference =2πr and Area =

${\pi \: r}^{2}$

It is given that circumference of circle is same as perimeter of square.

∴ Square's one side =

$\frac{1}{4}$

cirumference of the given circle

=

$\frac{1}{4} \times 2\pi \: r = \frac{\pi \: r}{2}$

∴ Area of square

$( \frac{\pi \: r}{2})^{2}$

So, Area of circle : Area of Square

${\pi \: r}^{2} :( \frac{\pi \: r}{2} ) {}^{2} = \frac{4}{\pi} = \frac{4}{ \frac{22}{7} } = \frac{14}{11}$