A) 1 : 1
B) \[2:\pi \]
C) \[\pi :2\]
D) \[\sqrt{\pi }:2\]
Correct Answer: D
Solution :
Let the radius of circle = r and side of square = x units. Then, \[\frac{\text{Area}\,\,\text{of}\,\,\text{circle}}{\text{Area}\,\,\text{of}\,\,\text{square}}=\frac{\pi {{r}^{2}}}{{{x}^{2}}}=1\] \[\Rightarrow \] \[{{x}^{2}}=\pi {{r}^{2}}\] \[\Rightarrow \] \[x=\sqrt{\pi }r\] Now, \[\frac{\text{Circumefrence}\,\,\text{of}\,\,\text{circle}}{\text{Perimeter}\,\,\text{of}\,\,\text{square}}=\frac{2\pi r}{4\sqrt{\pi }r}=\frac{\sqrt{\pi }}{2}\]
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