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Cover-up

Stage: 3 Short Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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.
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