A square and an equilateral triangle have equal perimeters. If the diagonal of the square is 12 2 cm, then the area of the triangle is :

Answer: Option D

Let the side of the square be a cm
Then, its diagonal = $$\sqrt{2}$$ a cm
Now, $$\sqrt{2}$$ a = $$12\sqrt{2}$$
⇒ a = 12 cm
Perimeter of the square = 4a = 48 cm
Perimeter of the equilateral triangle = 48 cm
Each side of the triangle = 16 cm
Area of the triangle :
$$\begin{array}{rl}& =\left(\frac{\sqrt{3}}{4}\times 16\times 16\right)c{m}^2\\ & =\left(64\sqrt{3}\right)c{m}^2\end{array}$$