Final answer:
To determine the possible integer lengths for the third side of a triangle with sides of 18 and 29 units, apply the triangle inequality theorem. The difference between the maximum potential length (46 units) and the minimum length (12 units) is 34 units.
Step-by-step explanation:
The question pertains to finding the minimum and maximum integer length of the third side of a triangle, given the two sides are 18 and 29 units long. To find this, we can use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side, and the difference of the lengths of any two sides must be less than the length of the third side.
For the maximum length, we have 18 + 29 = 47, implying that the third side must be less than 47 units. For the minimum length, we subtract the shorter side from the longer, so we have 29 - 18 = 11, meaning the third side must be greater than 11 units. Thus, the third side has to be an integer between 12 and 46 units.
The positive difference between the maximum and minimum integer lengths of the third side is therefore 46 - 12 = 34 units.