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?
A.
46 inches
B.
37 inches
C.
49 inches
D.
6 inches
To find the possible length of side AC, 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.
Given:
AB = 18 inches
BC = 26 inches
Now, we can find the range of possible lengths for AC:
AC > BC - AB
AC > 26 - 18
AC > 8
AC < BC + AB
AC < 26 + 18
AC < 44
Therefore, the possible length of side AC must be between 8 and 44 inches.
Looking at the options:
A. 46 inches - Not possible, exceeds the range
B. 37 inches - Possible
C. 49 inches - Not possible, exceeds the range
D. 6 inches - Possible
Therefore, the possible lengths of side AC are 6 inches and 37 inches. The correct answers are options B and D.