Which of the following are possible side lengths for a triangle? A. $8,13,1$ B. $16,11,7$ C. $2,3,5$ (1) sunny $^{9 \%}$ Copright zoos $_{2}$ - 2023 Intemational Academy of Science. All Rights Reserved

Step 1 ：In order for a set of three numbers to be the side lengths of a triangle, they must satisfy 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.

Step 2 ：We can apply this theorem to each of the given options to determine which are possible side lengths for a triangle.

Step 3 ：Checking option A: \(8 + 13 > 1\) and \(8 + 1 > 13\) and \(13 + 1 > 8\). The second condition is not satisfied, so option A is not a possible triangle.

Step 4 ：Checking option B: \(16 + 11 > 7\) and \(16 + 7 > 11\) and \(11 + 7 > 16\). All conditions are satisfied, so option B is a possible triangle.

Step 5 ：Checking option C: \(2 + 3 > 5\) and \(2 + 5 > 3\) and \(3 + 5 > 2\). The first condition is not satisfied, so option C is not a possible triangle.

Step 6 ：Final Answer: The only possible side lengths for a triangle from the given options are \(\boxed{16, 11, 7}\).