All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Shapes > Geometry
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)

Comments: ( Back to comment list | You must be logged in to post comments.)
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
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (14)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2024 by Animus Pactum Consulting. All rights reserved. Privacy Information