What is the size of the largest square which can fit inside a regular pentagon with a side-length of 1?
(In reply to re: More likely to be correct solution.
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