Answer:
The possible range of the length of side LM is 8 < x < 26 ⇒ A
Step-by-step explanation:
In any triangle:
- The sum of the lengths of any two sides must be greater than the length of the 3rd side
- The length of any side must greater than the difference of the lengths of the other two sides
- The difference of the other sides < The side < The sum of the other sides
In the given figure
∵ LMN is a triangle
∵ LM = x, MN = 9, NL = 17
→ Find the sum of the lengths of MN and NL
∴ The sum of the lengths of MN and NL = 9 + 17 = 26
→ Find the difference between the lengths of MN and NL
∴ The difference between the lengths of MN and NL = 17 - 9 = 8
→ By using the rules above, x should be between 8 and 26
∴ 8 < x < 26
∴ The possible range of the length of side LM is 8 < x < 26
