A) \[24\sqrt{2}\,c{{m}^{2}}\]
B) \[24\sqrt{3}\,c{{m}^{2}}\]
C) \[48\sqrt{3}\,c{{m}^{2}}\]
D) \[64\sqrt{3}\,c{{m}^{2}}\]
Correct Answer: D
Solution :
Diagonal of a square is \[12\sqrt{2}\,cm\] \[\Rightarrow \]\[2\sqrt{a}=12\sqrt{2}cm\Rightarrow a=12\,cm\] \[\therefore \]Perimeter of the square = 4a \[=4\times 12=48\,cm\] Perimeter of an equilateral triangle is 3a \[\Rightarrow 48\,cm=3a\Rightarrow a=\frac{48}{3}cm=16cm\] \[\therefore \]Area of equilateral triangle. \[=\frac{\sqrt{3}}{4}{{a}^{2}}=64\sqrt{3}\,c{{m}^{2}}\]
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