Final answer:
The triangle inequality theorem indicates that the length of side AB must be greater than 13 units and less than 35 units, so the inequality that describes all possible lengths of AB is 13 < AB < 35.
Step-by-step explanation:
The question is concerning the triangle inequality theorem, which relates to finding the range of possible lengths for the third side of a triangle when the lengths of two sides are known. According to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. We have a triangle ABC, with side AC measuring 11 units and side BC measuring 24 units.
To determine the range of possible lengths for side AB, we can apply the following inequalities:
AB + AC > BC
AB + BC > AC
AC + BC > AB
Simplifying these inequalities using the provided measurements, we get:
AB + 11 > 24
AB + 24 > 11
11 + 24 > AB
So, AB must be greater than 24 - 11, which is 13 units, and less than 11 + 24, which is 35 units.
Therefore, the inequality describing all possible lengths of AB is 13 < AB < 35.