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?

area of a square = a² sq cm

length of the diagonal =  $2a$ cm

area of equilateral triangle with side   $2a$= $\frac{3}{4}*2a2$
required ratio =  $\frac{3}{4}*2a2:a2=3:2$