Hi, here is how I would solve it:
1. first find the missing value for each perimeter listed under options I-III.
I. 2+5+2=9 (2 is the missing leg)
II. 2+5+8=15 (8 is the missing leg)
III. 2+5+12=19 (12 is the missing leg)
2. Find which options could be a valid triangle based on the rule that the sum of the two shorter sides must be greater than the longest side.
I. 2+2>5 Not Valid
II. 2+5>8 Not Valid
III. 2+5>12 Not Valid
Assuming I am thinking straight, the answer is "None"