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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 More likely to be correct solution. | Comment 2 of 4 |
I should have tried putting a corner of the square into a corner of the pentagon.  The problem this time is I have the square standing up straight.   This is an improvement but not the best yet.

The height of the pentagon is sin(72)+sin(36)
if you divide this by the √2 diagonal of the square you get
.25(√(5+√5)+√(5-√5))≈1.0881

You can improve this by rotating the square by 9
(divide by cos(9))
≈ 1.1017

  Posted by Jer on 2013-12-02 16:15:39
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