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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

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