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
re: Geometer's Sketchpad Solution by Jer)
I used the following property:
If XYZ is the triangle, then the crease length of folding
vertex X to vertex Y is
(XY/2) * tan( min( angle X , angle Y ) )
My first solution comes from A < C < B. Thus
7 = crease length A > B
= (c/2)*tan(A)
8 = crease length A > C
= (b/2)*tan(A)
therefore, c = (7/8)b
My second solution comes from B < C < A. Thus
7 = crease length A > B
= (c/2)*tan(B)
9 = crease length B > C
= (a/2)*tan(B)
therefore, c = (7/9)a
My third solution comes from C < B < A. Thus
8 = crease length A > C
= (b/2)*tan(C)
9 = crease length B > C
= (a/2)*tan(C)
therefore, b = (8/9)a
The only problem with the third solution
was that it cannot be constructed.

Posted by Bractals
on 20120522 01:53:27 