Question

If a triangle has lengths of 8 and 17, check all the possible lengths for the third side.

A. 09
B. 13
C. 0 17
D. 23

Answer 1

The possible lengths for the third side of the triangle are 9 and 23.

Step-by-step explanation:

To find the possible lengths for the third side of a triangle with lengths 8 and 17, we need to use the triangle inequality theorem. According to the theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. So in this case, we can check which options satisfy the condition:

• Option A: 9 - 8 + 9 = 17 (satisfied)
• Option B: 13 - 8 + 13 = 18 (not satisfied)
• Option C: 0 - 8 + 0 = -8 (not satisfied)
• Option D: 23 - 8 + 23 = 38 (satisfied)

Therefore, the possible lengths for the third side are 9 and 23 (options A and D).