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Take five (Posted on 2011-05-22) Difficulty: 4 of 5
A triangle is Heronian if all its sides and its area are integers.
Any such rational triangle can be scaled up to a corresponding triangle with integer sides and area, and often the term Heronian triangle is used to refer to the latter.
There are only 5 Heronian triangles (with all sides being integers) whose perimeters numerically are equal to their areas.

You are requested to find all of them.

  Submitted by Ady TZIDON    
Rating: 3.6667 (3 votes)
Solution: (Hide)
1. ( 6, 8, 10) Area = Perimeter = 24
2. ( 5, 12, 13) Area = Perimeter = 30
3. ( 9, 10, 17) Area = Perimeter = 36
4. ( 7, 15, 20) Area = Perimeter = 42
5. ( 6, 25, 29) Area = Perimeter = 60
Copied from Dej Mar's solution

Comments: ( You must be logged in to post comments.)
  Subject Author Date
SolutionRest time overDej Mar2011-05-22 17:55:57
Left trianglesMath Man2011-05-22 15:30:15
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