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 :
Options:
A . $$24\sqrt 2 $$ cm2
B . $$24\sqrt 3 $$ cm2
C . $$48\sqrt 3 $$ cm2
D . $$64\sqrt 3 $$ cm2
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 : $$\eqalign{ & = \left( {\frac{{\sqrt 3 }}{4} \times 16 \times 16} \right)c{m^2} \cr & = \left( {64\sqrt 3 } \right)c{m^2} \cr} $$
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