As in the previous cases the formula for the area has been considered.
If the perimeter is less than or equal to 100, then the semi-perimeter is less than or equal to 50. If the prime factor is greater than 10, then it must be less than or equal to 47 by the same logic. Due to the size of the prime number factor, there are no possible values for a that will result in (s - a) equal to the prime factor and still allow for values of b and c that will yield squares and meet the triangle inequality.
Again, this is a proposition and not a proof. I suspect based on the other patterns I observed from this exercise that as the perimeter increases, there will be increasingly more possibilities for integral triangles, and that this particular pattern was observed only due to the small portion of the integers observed and the limitations of the triangle inequality.