We use following two properties of triangles
1)for otbuse triangle pythagoras thm says that
c^2>a^2+b^2
2)sum of two sides greater than third side
case 1:so if x is bigger
x<15+8 ie 23
x can take values 15 16 17 18 19 20 21 22
15^2+8^2=17^2
so x can take values 18 19 20 21 22 only
case 2:if x is not bigger
15<x+8 x>7 ie 8 9 10 11 12 13 14
15^2>x^2+8^2
x^2<225-64
x^2<161
so x take values 8 9 10 11 12
so total 10 values possible for x