Final answer:
A triangle cannot be formed with side lengths 15, 7, and 6 because the sum of any two sides must be greater than the third side (7 + 6 < 15), according to the Triangle Inequality Theorem.
Step-by-step explanation:
To determine if a triangle can be formed with side lengths 15, 7, and 6, we can use 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, we can examine the given side lengths:
- 7 + 6 = 13, which is less than 15
- 7 + 15 = 22, which is greater than 6
- 6 + 15 = 21, which is greater than 7
Given that one of these sums (7 + 6) is not greater than the third side (15), a triangle cannot be formed with side lengths 15, 7, and 6.
The correct answer is a) No, because 7 + 6 < 15.