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

A. $$24\sqrt 2 $$ cm²

B. $$24\sqrt 3 $$ cm²

C. $$48\sqrt 3 $$ cm²

D. $$64\sqrt 3 $$ cm²

Answer: Option D

Solution(By Examveda Team)

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 :
$$\eqalign{ & = \left( {\frac{{\sqrt 3 }}{4} \times 16 \times 16} \right)c{m^2} \cr & = \left( {64\sqrt 3 } \right)c{m^2} \cr} $$