To determine the length of the third side of a triangle given the lengths of two sides, you 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 denote the lengths of the sides you provided:
- Side A = 18
- Side B = 16
- Side C = unknown
According to the triangle inequality theorem, the following three conditions must be satisfied:
- A + B > C
- A + C > B
- B + C > A
Using these inequalities, let's denote the unknown side as C.
- \( 18 + 16 > C \) implies \( C < 34 \).
- \( 18 + C > 16 \) implies \( C > -2 \) (which is always true since lengths are positive).
- \( 16 + C > 18 \) implies \( C > 2 \).
From this, we know:
- \( 2 < C < 34 \)
The actual value of C can vary depending on the specific triangle you are trying to form. However, since you only provided the lengths of two sides and no additional context, we cannot find the exact length of the third side.
If you meant for the third side to be computed in a specific context (like a right triangle), please clarify. Otherwise, C can be any value between 2 and 34. If you select any specific length within that range (for example, 10 or 30), please let me know!