The possible lengths for the third side are 47, 18, 24, 8, and 44.
To determine whether a set of three side lengths can form a triangle, we can use 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.
Let's apply this theorem to the given side lengths (18, 26, and the options):
18 + 26 > Third Side
44 > Third Side
18 + Third Side > 26
Third Side > 8
26 + Third Side > 18
Third Side > -8 (This is always true because lengths cannot be negative.)
Now, let's check each option:
47: 44 < 47 (This is true.)
18: 8 < 18 (This is true.)
24: 8 + 24 > 18 (This is true.)
8: 18 + 8 > 26 (This is true.)
44: 18 + 44 > 26 (This is true.)
Therefore, the possible lengths for the third side are 47, 18, 24, 8, and 44.