A) \[A\le \frac{{{s}^{2}}}{3\sqrt{3}}\]
B) \[A=\frac{{{s}^{2}}}{2}\]
C) \[A>\frac{{{s}^{2}}}{\sqrt{3}}\]
D) none of these
Correct Answer: A
Solution :
| For a given perimeter an equilateral triangle has the maximum area |
| \[\Rightarrow \] \[{{A}_{\max }}=\frac{\sqrt{3}}{4}\,\,{{\left( \frac{2s}{3} \right)}^{2}}=\frac{{{s}^{2}}}{3\sqrt{3}}\] |
| \[\Rightarrow \] \[A\le {{A}_{\max }}.\] |
| \[\Rightarrow \] \[A\le \frac{{{s}^{2}}}{3\sqrt{3}}\] |
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