An equilateral triangle is described on the diagonal of a square. What is the ratio of the area of the triangle to that of the square ?

Answer: Option C

Let the side of the square be a cm

Then, the length of its diagonal = $$\sqrt{2}$$ a cm
Area of equilateral triangle with side :
$$\begin{array}{rl}& =\sqrt{2}a\\ & =\frac{\sqrt{3}}{4}\times {\left(\sqrt{2}a\right)}^2\\ & =\frac{\sqrt{3}{a}^2}{2}\end{array}$$
∴ Required ratio :
$$\begin{array}{rl}& =\frac{\sqrt{3}{a}^2}{2}:a^2\\ & =\sqrt{3}:2\end{array}$$