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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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re(2): More likely to be correct solution. Comment 4 of 4 |
(In reply to re: More likely to be correct solution. by Jer)

I agree.

Construction: Construct pentagon ABCDE with centre O. Construct a line perpendicular to AO and bisect both angles to AO with lines passing through BC at F and DE at H, to form 2 sides of the square. Lines perpendicular to AF and AH will meet at G to complete the square AFGH.

The area of the square is 5-5^(1/2)-(5 (5-2*5^(1/2)))^(1/2). The ratio of the pentagon to the square is (5^(1/2)+(2*(5+5^(1/2)))^(1/2))/4 to 1, almost exactly 1.51 times the size.

Edited on December 3, 2013, 6:32 am
  Posted by broll on 2013-12-03 06:27:14

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