The addition of the lengths of two sides of a triangle must be greater than the length of the third side. For example, if the lengths are a, b, and c, then:
a + b > c
a + c > b
b + c > a
If three lengths are given we can check this criterium, simply adding the lengths of the shorter sides and checking if their addition is greater than the third side.
Case: 9,8,7
8 + 7 > 9
15 > 9
then, 9,8,7 can be the sides of a triangle.
Case: 10, 5, 14
10 + 5 > 14
15 > 14
then, 10, 5, 14 can be the sides of a triangle.
Case: 17.5, 3.0, 14.0
14 + 3 > 17.5
17 > 17.5
This inequality is not satisfied, then 17.5, 3.0, 14.0 cannot be the sides of a triangle.
Case: 32, 10, 16
10 + 16 > 32
26 > 32
This inequality is not satisfied, then 32, 10, 16 cannot be the sides of a triangle.