Final answer:
The range of the third side of a triangle, given two sides are 7 and 10, is 3 to 17 units according to the Triangle Inequality Theorem.
Step-by-step explanation:
When given the measures of two sides of a triangle, the possible range of values for the third side can be found using the Triangle Inequality Theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Therefore, for a triangle with side lengths 7 and 10, the third side must be greater than 10 - 7 = 3 and less than 10 + 7 = 17. This means the possible range of values for the third side is 3 to 17 units. None of the listed options (7 and 10, 5 to 15, 7 to 10, 12.5 to 32.5) are correct; the correct range would have to reflect this theorem.