In triangle ABC, the length of side AB is 18 inches and the length of side BC is 26 inches. Which of the following could be the length of side AC?(2 points)
Responses
46 inches
46 inches
31 inches
31 inches
49 inches
49 inches
6 inches
Based on the triangle inequality theorem, for any triangle ABC, the sum of the lengths of any two sides must be greater than the length of the third side.
In this case, the length of side AB is 18 inches and the length of side BC is 26 inches. Therefore, to find the possible lengths of side AC, we need to check if the sum of these two sides is greater than the third side.
18 + 26 = 44
In this case, the sum of 18 inches and 26 inches is 44 inches. Since 44 inches is not greater than 46 inches or 31 inches or 49 inches, these are not possible lengths for side AC.
However, 44 inches is greater than 6 inches. Therefore, side AC could possibly be 6 inches.