Integer right triangles

If \( p \) is the perimeter of a right angle triangle with integral length sides, \( \{a,b,c\} \), there are exactly three solutions for \( p=120 \).

\( \{20,48,52\}, \{24,45,51\}, \{30,40,50\} \)

For which value of \( p \leq 1000 \), is the number of solutions maximised?