There are only five integer-sided triangles in which the area equals the perimeter:
(5, 12, 13) (6, 8, 10) (6, 25, 29) (7, 15, 20) (9, 10, 17)
Only two of them are right triangles.
(Lee Markowitz, “Area = Perimeter,” Mathematics Teacher 74:3 [March 1981], 222-223.)