This problem is testing the triangle property that states that 2 sides summed together must be bigger than the third side.

Let's find what the third side could be:


1. 6 or smaller. This is because 2 + 5 = 7, so the third side must be smaller than 7

2. 4 or bigger. This is because the second side is 5, so the first and third together must be bigger and 2 + 4 = 6

Combining these two, we know the range, and that the third side can only be 4, 5, or 6.

The perimeter then could be one of these three:
2 + 5 + 4 = 11
2 + 5 + 5 = 12
2 + 5 + 6 = 13

None of these value appear so the answer is A.

In a triangle sum of two side greater than 3 rd side,
Here we have 5,2
sum(5+2) = 7

3rd side <7> 5
3 can come as 2+3 = 5 isosceles
perimeter can 5+2+4=11 or 5+5+2=12
so answer is none.