If I place a triangle on a $6$cm by $6$cm square, I can cover up to $2\over 3$ of the square.
If I place the square on the triangle, I can cover up to $60$% of the triangle.
What is the area of the triangle?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.
View the archive of all weekly problems grouped by curriculum topic

View the previous week's solution
View the current weekly problem