Euclidean cover up

A 6 cm × 6 cm square when placed on a triangle, can cover up to 60% of the triangle. If the triangle is placed on the square, it can cover up to $\frac{2}{3}$ of the square. What is the area, in cm$^2$, of the triangle?

This problem from the British Columbia Colleges Senior High School Contest for 2000

Ans: 40 cm2