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 Triangular Crease 789 (Posted on 2012-05-20)
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)

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 re(2): Geometer's Sketchpad Solution | Comment 4 of 7 |

`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 solutionwas that it cannot be constructed.`

 Posted by Bractals on 2012-05-22 01:53:27

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