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.

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

Edited on May 23, 2011, 4:56 pm

Posted by Dej Mar on 2011-05-22 17:55:57