The number of acute angled triangles whose sides are three consecutive positive integers and whose perimeter is at most 100 is

Sides n-1,n,n+1; acute iff (n+1)^2<(n-1)^2+n^2, i.e. n^2>4n, n>4 (n=4 gives right triangle 3,4,5). Perimeter 3n<=100 gives n<=33. n=5..33: 29 triangles.