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Square in a Pentagon (Posted on 2013-12-01) Difficulty: 3 of 5
What is the size of the largest square which can fit inside a regular pentagon with a side-length of 1?

No Solution Yet Submitted by Danish Ahmed Khan    
Rating: 3.0000 (1 votes)

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Solution re: More likely to be correct solution. | Comment 3 of 4 |
(In reply to More likely to be correct solution. by Jer)

That's not right.  The square in a corner cannot stretch all the way to the opposite side.  The other corners are a bit too wide.

I don't know why I tried doing this without the aid of GSP.
I used Geometer's Sketchpad to shrink the square a bit and it now looks like the best solution is 1.0674

Edit:  The exact solution is sin(108)/sin(63)
=√(5-√5-√(5(5-2√5)))

Edited on December 3, 2013, 12:54 am
  Posted by Jer on 2013-12-03 00:44:35

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