The possible lengths for the third side are 47, 24, and 44.
The triangle inequality theorem can be applied. The theory states that any triangle's two side lengths added together must be bigger than its third side's length.
Let's examine your options:
- A: 47 - B: 18 (side length previously specified)
- C: 24, D: 8, and E: 44
We must add each choice to one of the provided side lengths and determine whether the total is more than the other side length in order to determine whether the third side can have any length at all.
- Option A is a valid length because 18 + 47 = 65 is greater than 26.
- Option B is not a valid length because 18 + 18 equals 36 (not larger than 26).
- Option C is a valid length because 18 + 24 = 42 is greater than 26.
- Option D is not a valid length because 18 + 8 equals 26 (identical to 26).
- Option E is a valid length because 18 + 44 = 62 is greater than 26.
So, the possible lengths for the third side are 47, 24, and 44.