The diagonal of a square equals the side of an equilateral triangle. If the area of the square is 12 sq cm, what is the area of the equilateral triangle?

Let the side of square = $$s$$ cm and diagonal = $$d$$ cm

=> Area of square = $$(s)^2 = 12$$ ----------(i)

In right triangle of the square, => $$(s)^2 + (s)^2 = (d)^2$$

Substituting value of $$s^2$$ from equation (i)

=> $$(d)^2 = 12 + 12 = 24$$ ----------(ii)

Side of equilateral triangle = Diagonal of square = $$d$$ cm

$$\therefore$$ Area of equilateral triangle = $$\frac{\sqrt{3}}{4} d^2$$

Substituting value of $$d^2$$ from (ii), we get :

= $$\frac{\sqrt{3}}{4} \times 24 = 6\sqrt{3} cm^2$$

=> Ans - (B)