Final answer:
Using the Triangle Inequality Theorem, it was found that the set of side lengths that will NOT create a triangle is the set b (2, 5, 8), because 2 + 5 is not greater than 8.
Step-by-step explanation:
To determine which set of side lengths will NOT create a triangle, 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. We can check each set of given side lengths:
- For set a (8, 9, 10): 8 + 9 > 10, 8 + 10 > 9, and 9 + 10 > 8, so these side lengths can create a triangle.
- For set b (2, 5, 8): 2 + 5 is not greater than 8, which means this set cannot create a triangle.
- For set c (10, 15, 20): 10 + 15 > 20, 10 + 20 > 15, and 15 + 20 > 10, so these side lengths can create a triangle.
- For set d (10, 14, 18): 10 + 14 > 18, 10 + 18 > 14, and 14 + 18 > 10, so these side lengths can create a triangle.
Therefore, the set of side lengths that will NOT create a triangle is set b (2, 5, 8).