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Square of Triangles (Posted on 2006-02-04) Difficulty: 4 of 5
Given a partition of a square into n triangles of equal area, prove that n is even.

No Solution Yet Submitted by Josh70679    
Rating: 2.0000 (2 votes)

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Equal area, congruent triangles. | Comment 2 of 21 |
We can divide a square into 3 triangles by joining two adjacent vertices to the midpoint of the opposite side.  This gives us two congruent triangles while the larger is twice the area of each of the other two.

An initial thought was that  all triangles would have to be  congruent, which would mean that the large triangle would have to be bisected yielding 4 identical triangles.  However I note that this large triangle can be divided into two equal areas by joining one of vertices (which it shares with the square) to the midpoint of the opposing side.

I am sure that this is not going to assist in the solution, but I felt that the observation might be of interest.

  Posted by brianjn on 2006-02-04 17:57:27
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