The Triangle Inequality Theorem
If two side lengths of a triangle are given, the third side cannot have any unbounded length.
The triangle inequality theorem rules the possible values for the length of the unknown side.
Suppose we are given two side lengths a and b. If they form a triangle and we set the angle between them very close to 0, then the length of the third side, call it c, cannot be less than a-b (provided a is greater than b). Writing it as an inequality: a - b < c.
Now suppose the angle between a and b is very close to 180°. then the length of c must be enough to almost match the sum of a+b. Writing this condition as an inequality: a + b > c.
Joining both conditions in a single inequality:
a - b < c < a+b
The unknown length is x and a= 17 b=14, thus:
17 - 14 < x < 17 + 14
Operating:
3 < x < 31