A) 8 cm
B) 9 cm
C) 4 cm
D) 12 cm
E) None of these
Correct Answer: C
Solution :
Explanation Option [c] is correct. The area of an equilateral triangle \[=\frac{\sqrt{3}}{4}\times {{(side)}^{2}}.\] Hence, \[4\sqrt{3}=\frac{\sqrt{3}}{4}\times {{(\operatorname{si}de)}^{2}}\] \[\Rightarrow 4\sqrt{3}=\frac{\sqrt{3}\times {{(\operatorname{si}de)}^{2}}}{4}\Rightarrow 4\sqrt{3}\times 4=\sqrt{3}\times {{(side)}^{2}}.\] \[\Rightarrow {{(side)}^{2}}=\frac{4\sqrt{3}\times 4}{\sqrt{3}}=16\Rightarrow side=\sqrt{16}=4cm.\]
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