A square and an equilateral triangle have the same perimeter. If the diagonal of the square is $$12 \surd2$$ cm, then the area of the triangle is

Let the perimeter of square and equilateral triangle be $$12x$$ cm

=> Each side of square = $$\frac{12x}{4}=3x$$ cm and each side of equilateral triangle = $$4x$$ cm

Diagonal of a square = $$d=\sqrt2\times$$ side

=> $$3x\times\sqrt2=12\sqrt2$$

=> $$x=\frac{12}{3}=4$$

=> Side of equilateral triangle = $$4\times4=16$$ cm

$$\therefore$$ Area of equilateral triangle = $$\frac{\sqrt3}{4} s^2$$

= $$\frac{\sqrt3}{4}\times(16)\times(16)$$

= $$64\sqrt3$$ $$cm^2$$

=> Ans - (C)