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The diagram shows an irregular hexagon with interior angles all equal to 120 degrees made by cutting the corners off a piece of card in the shape of an equilateral triangle with sides of length 20 units.

An identical hexagon could also be made by cutting the corners off a different equilateral triangle.

What is the side length of this 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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