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

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

To do: To find the ratio of their areas.

Solution:

As 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 & $a$ be the side of square, then

$2\pi r=4a$

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

Now, $\frac{Area\ of\ the\ circle}{Area\ of\ the\ square}=\frac{\pi r^2}{a^2}$

$\Rightarrow \frac{Area\ of\ the\ circle}{Area\ of\ the\ square}=\frac{\pi\times2^2}{\pi^2}$

$=\frac{4}{\pi}$

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

Tutorialspoint

Simply Easy Learning

Updated on: 10-Oct-2022

8K+ Views
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}