A) 1cm
B) \[\sqrt{3}\]
C) 3 cm
D) \[\sqrt{3}+2\,cm\]
Correct Answer: A
Solution :
If x is the side of an equilateral triangle, then its area \[{{A}_{1}}=\frac{{{x}^{2}}\sqrt{3}}{4}\] If each side is increased by 2, then area of the triangle \[{{A}_{2}}=\frac{{{(c+2)}^{2}}\sqrt{3}}{4}\] But \[{{A}_{2}}={{A}_{1}}+2\sqrt{3}\] therefore \[\frac{{{(x+2)}^{2}}\sqrt{3}}{4}=\frac{{{x}^{2}}\sqrt{3}}{4}+2\sqrt{3}\] or \[4x+4=8\] or \[x=1\,cm\]
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