4. Which of the following could not be the side lengths of a triangle?
A. 9, 5, 5
B. 4, 9, 5
C. 4, 3,6
The side lengths of a triangle must follow 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.
For option A, the side lengths are 9, 5, and 5. The sum of the two shorter sides (5 + 5 = 10) is greater than the length of the longest side (9). Therefore, option A could be the side lengths of a triangle.
For option B, the side lengths are 4, 9, and 5. The sum of the two shorter sides (4 + 5 = 9) is equal to the length of the longest side (9). Therefore, option B could be the side lengths of a degenerate triangle, which is a triangle with all three sides on the same line. It is not a traditional triangle, but it is still considered a triangle.
For option C, the side lengths are 4, 3, and 6. The sum of the two shorter sides (3 + 4 = 7) is not greater than the length of the longest side (6). Therefore, option C could not be the side lengths of a triangle.
Therefore, the answer is:
C. 4, 3, 6