Final answer:
The length of the third side of the triangle could be 28 cm.
Step-by-step explanation:
In a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. So, in this case, the length of the third side must be greater than the difference between the two given lengths and less than the sum of the two given lengths.
Given that the lengths of the two sides are 9 centimeters and 37 centimeters, we can calculate the possible range for the length of the third side:
37 - 9 = 28 cm
9 + 37 = 46 cm
Therefore, the possible length of the third side of the triangle is between 28 centimeters and 46 centimeters. From the options given, the only value within this range is Option B: 28 cm.