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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.*