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I squeeze, squeeze, and squeeze (Posted on 2019-02-15) Difficulty: 3 of 5
Put three congruent triangles inside a unit square so that they don't overlap one another.

What is the maximum possible area of one of the triangles?

No Solution Yet Submitted by Danish Ahmed Khan    
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Solution Actual solution | Comment 3 of 4 |
Not sure why I assumed equilateral triangles.

For any three triangles:

Make them right triangles with their 30 degree angles making up one angle of the square.  The longer leg of two of them are sides of the square.  The third sits in the middle gap.  

Each triangle has area sqrt(3)/6.

Together they take up sqrt(3)/2 of the triangle which is better than the trivial 3/4.

  Posted by Jer on 2019-02-17 13:20:08
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