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Two Triangles Divided (Posted on 2007-12-16) Difficulty: 3 of 5
There are two triangles ABC, and A'B'C'. The bases are AB and A'B'.

Triangle ABC has an altitude drawn from C to AB, meeting the base at point P. This altitude divides the triangle into two unequal right triangles.

Triangle A'B'C' also has a point, P' on its base, with a line segment connecting it to vertex C', but chosen so that angle A'P'C' is 60, with the resulting triangle A'P'C' though, not being equilateral.

All eight line segments are of integer length, and each triangle has a perimeter less than 50. The bases, AB and A'B', are the longest sides in each of the two respective original triangles, and they differ by 1 unit in length.

  • What are the dimensions of the triangles ABC and A'B'C'?
  • What are the lengths of CP and C'P'?

See The Solution Submitted by Charlie    
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  Subject Author Date
Solutionre: Answer (Solution)DJ2007-12-17 21:45:11
SolutionSolutionDej Mar2007-12-17 21:03:37
SolutionAnswerDJ2007-12-17 17:30:26
Partial SolutionPraneeth2007-12-17 01:43:57
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