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?
Correct Answer: Option D
area of a square = a² sq cm
length of the diagonal = \(\sqrt{2a}\) cm
area of equilateral triangle with side \(\sqrt{2a}\) = \(\frac{\sqrt3}4\ast\left(\sqrt{2a}\right)^2\)
required ratio = \(\frac{\sqrt3}4\ast\left(\sqrt{2a}\right)^2:a^2=\sqrt3:2\)
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