The legs of a triangle measure 13 centimeters and 17 centimeters. Which of the following is the measure for the longest side of the triangle? A. 29 cm B. 30 cm C. 31 cm D. 4 cm

To find the measure of the longest side of the triangle, 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. In this case, we add the lengths of the legs: 13 cm + 17 cm = 30 cm. Therefore, the longest side must be less than 30 cm, and we can eliminate options A (29 cm) and B (30 cm), as they are possible lengths. The answer must be C (31 cm), which is not a valid option since it exceeds the sum of the two legs. To analyze the options further, we can see that the only possible lengths for the longest side must be less than 30 cm. Thus, the longest side can only be option A (29 cm). Happy triangle solving!