A) \[36\sqrt{2}\]
B) \[36\sqrt{3}\]
C) \[64\sqrt{2}\]
D) \[64\sqrt{3}\]
Correct Answer: D
Solution :
Since a diagonal of the square is \[12\sqrt{2}\,cm,\] Length of a side of square \[12\sqrt{2}\,\times \left( \frac{1}{\sqrt{2}} \right)=12\,cm.\]. Perimeter of the square \[=12\times 4=48\text{ }cm\] \[\therefore \] Perimeter of the equilateral triangle \[=48\text{ }cm,\] Hence each side\[~=16\text{ }cm\] and, area \[=\frac{1}{2}\times {{(16)}^{2}}\times \frac{\sqrt{3}}{2}\] \[=64\sqrt{3}\,c{{m}^{2}}\]
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