A square and an equilateral triangle have the same perimeter If the diagonal of the square is 6 2 cm...........

Quantitative Aptitude (CDS) Mensuration 2D

A square and an equilateral triangle have the same perimeter. If the diagonal of the square is 6 2 cm, then what is the area of the triangle?

$12\sqrt{2}\: cm^{2}$

$12\sqrt{3}\: cm^{2}$

$16\sqrt{2}\: cm^{2}$

$16\sqrt{3}\: cm^{2}$

Let Side of triangle = a & Side of Square = b

According to question, 3a =4b (Since their perimeters are same)

Diagonal of square = b√2 = 6√2 Hence, b= 6 So, a = 8

Area of triangle = √3/4 a2

= √3/4 * 64 =16 √3

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