Understand & Think: The problem is asking for a triangle with the given side lengths that cannot exist. This means that the side lengths are not valid for creating a triangle. I know that in order for a triangle to exist, the sum of the lengths of any two sides must be greater than the length of the third side. I will try to find a combination of side lengths that does not satisfy this condition.
Do/Answer: The combination of side lengths that does not satisfy the condition is 9, 11, and 10. According to the triangle inequality theorem, the sum of the lengths of any two sides must be greater than the length of the third side. However, in this case, 9 + 11 is equal to 20, which is not greater than 10. Therefore, a triangle with side lengths 9, 11, and 10 cannot exist.
Explanation of my answer and why it makes sense: This answer makes sense because it follows 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. In this scenario, the sum of 9 and 11 is not greater than 10, so a triangle cannot be formed using these side lengths.