Description for Correct answer:
If r is the radius of the circle, then

area of the circle = \( \Large \pi r^{2} = 100 \pi cm^{2} \)

=> \( \Large r^{2} = 100 \) ...(i)

=> \( \Large r = 10 cm \)

From the given figure,

\( \Large x^{2}+x^{2}=r^{2} \)

=> \( \Large 2x^{2}=r^{2} \) ...(ii)

side of the square = 2x

=\( \Large 2\sqrt{\frac{r^{2}}{2}}=\sqrt{2}r=10\sqrt{2} cm \)