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Triangular Crease 789 (Posted on 2012-05-20) Difficulty: 3 of 5
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.

No Solution Yet Submitted by K Sengupta    
Rating: 5.0000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts re(2): Geometer's Sketchpad Solution | Comment 4 of 7 |
(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 2012-05-22 01:53:27
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