A piece of paper has the precise shape of a triangle (which we will denote by triangle ABC), where the respective lengths of the crease whenever the paper is folded such that; the vertex A is joined onto vertex B, the vertex A is joined onto vertex C and, the vertex B is joined onto vertex C are 7, 8 and 9.

Determine the lengths AB, AC and BC.

(In reply to Geometer's Sketchpad Solution by Bractals)

Our first solutions match, but our seconds do not.  My second solution has two side lengths over 100. 


Incidentally, I had a third solution which I assume is extraneous since my two points would have imaginary x coordinates.  I had ignored it but here's what happens:
(28.02i, 19.47) (51.03i, 19.47)
and assuming we can even use the distance formula the side lengths become
20.15i, 47.17i, 23.01i
this makes even less sense because it doesn't work in the triangle inequality.

Posted by Jer on 2012-05-21 13:52:24