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'Cover-up' printed from http://nrich.maths.org/
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?
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which challenges you to use similar mathematical ideas.
This problem is taken from the UKMT Mathematical Challenges.