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Equilateral triangles are constructed on its four sides, as shown.  The side length of the large square is 1.  What is the side length of the small square?

 

 Oct 10, 2020
 #1
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The side length of the small square is 2 - sqrt(3).

 Oct 10, 2020
 #2
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Side  a = (1/2) / cos(15º)

 Oct 11, 2020

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