Question

Two sides of a triangle have lengths of 18 and 29 units. if the third side has an integer length, what is the positive difference between the maximum and minimum length of the third side?

Answer 1

Triangular inequality:  Length of third side must be less than the sum of the lengths of the other 2 sides.
x < 18 + 29
x < 47

so Maximum length of third side is 46 units.

Also 29 < 18 + x
x > 11    so minimum length = 12

Difference  = 46-11 = 35