A) \[\frac{\pi {{s}^{2}}}{9}\]
B) \[\frac{3{{s}^{2}}}{\pi }\]
C) \[\frac{3s}{\pi }\]
D) \[\frac{3\sqrt{3s}}{\pi }\]
Correct Answer: D
Solution :
If the side of the triangle be a cm, then \[S=\frac{{{a}^{2}}\sqrt{3}}{4}\] or \[{{a}^{2}}=\frac{4S}{\sqrt{3}}\] and the perimeter of the triangle \[=3a\] \[\therefore \] Circumference of the circle \[=3a\] \[\therefore \] If r be the radius of the circle, \[2\pi \,\,r=3a\] \[\therefore \] \[r=\frac{3a}{2\pi }\] \[\therefore \]Area of the circle \[=\pi \,{{r}^{2}}\] \[=\pi \times \frac{9{{a}^{2}}}{4{{\pi }^{2}}}=\frac{9}{4\pi }\times \frac{4S}{\sqrt{3}}\] \[=\frac{3\sqrt{3}\,S}{\pi }\]
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