Final answer:
The set of numbers that could not represent the sides of a triangle fails to meet the Triangle Inequality Theorem, where the sum of any two sides must be greater than the length of the third side.
Step-by-step explanation:
To determine which set of numbers could not represent the sides of a triangle, you must apply the Triangle Inequality Theorem. This theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side. Therefore, for a set of three numbers to represent the sides of a triangle, the sum of every pair of numbers must be greater than the third number.
For example, if you are given three numbers, say 5, 12, and 18, you can apply the theorem:
5 + 12 > 18 (True)
5 + 18 > 12 (True)
12 + 18 > 5 (True)
However, in this case, the first statement is not true (5 + 12 is not greater than 18), which means that these numbers could not represent the sides of a triangle.
Additionally, recall that a triangle is a three-sided figure lying on a plane with three angles adding up to 180 degrees. This relates to angles, but it's essential to separate this concept from the Triangle Inequality Theorem, which deals solely with the sides' lengths.