Question

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

Answer 1

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

$2\pi r=4a$

$[\frac{r}{a}=\frac{4}{2\pi }=\frac{2}{\pi }]$

Now $\frac{Areaofcircle}{Areaofsquare}=\frac{\pi r^2}{a^2}=\pi {\left(\frac{r}{a}\right)}^2$

Using $\frac{r}{a}=\frac{2}{\pi }$, we get

$\frac{A_{circle}}{A_{square}}=\pi {\left(\frac{2}{\pi }\right)}^2=\frac{4}{{\pi }^2}\times \pi =\frac{4}{\pi }$

Hence the ratio of Area of a circle to that of a square is $\frac{4}{\pi }$.