## Integer right triangles

### Problem 39

Published on Friday, 14th March 2003, 06:00 pm; Solved by 44167; Difficulty rating: 5%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* ≤ 1000, is the number of solutions maximised?