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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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Possible solution | Comment 1 of 4
Assuming the best orientation is with one side of the square parallel to one side of the pentagon the side length can be found using the law of sines on a couple of triangles formed.

The side comes out to be sin(108)/(sin(36)+sin(18))
=√5 - .5√(10-2√5) ≈ 1.0605

  Posted by Jer on 2013-12-02 15:58:05
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