A) \[\pi :\sqrt{3}\]
B) \[\pi :3\]
C) \[\pi :9\]
D) \[\pi :3\sqrt{3}\]
Correct Answer: D
Solution :
If perimeter of an equilateral triangle is p, then each side is of length \[\frac{p}{3},\] and area \[=\frac{1}{2}{{\left( \frac{p}{3} \right)}^{2}}\frac{\sqrt{3}}{2}=\frac{{{p}^{2}}\sqrt{3}}{36}\] If perimeter of a circle is p, then its radius is \[\frac{p}{2\pi }\] and area \[=\pi {{\left( \frac{p}{2\pi } \right)}^{2}}=\frac{{{p}^{2}}}{4\pi }\] \[\therefore \] Required ratio \[=\frac{{{p}^{2}}\sqrt{3}}{36}\,:\,\frac{{{p}^{2}}}{4\pi }=\pi :3\sqrt{3}\]
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