A square inscribed in a pentagon. A geometry puzzle

This video is about a square and a pentagon
If you need to post a picture of your solution or idea:
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EXPLORE:

[ybodoN]

I was thinking of a puzzle with a pentagon,
... and here you come with a very nice one!

[geoffreyparfitt]

My answer is 1.0605 (5 sig fig) . I think surds within surds may be exact but not so meaningful.

[attila]

what if the square was tilted. is it given top sides of pentagon and square is parallel?

[backgammonmaster]

Hi, Is this the largest square that can fit in a unit pentagon? if yes, any proof? Thanks

[pk]

I liked the video . You just made one little slip up at the end . The formula you derived for x had a 2 in the denominator . When you applied your derived formula, you said 1 in the denominator . You should have said 2 .

[sirmeowthelibrarycat]

😡 If you repeat ‘cool’ once more I will be frozen to death. It is a very irritating habit, detracting from the issue being explained. I will not subscribe to this channel.