Draw two isosceles triangles and label them:

 Leg 1   +    Leg 2   +    Base   =  Perimeter 

  2a     +     2a     +     b     =   4a + b

  b/2    +    b/2     +    4a     =   4a + b

In the first case 4a must be greater than b, by the
triangle inequality.

In the second case, b must be greater than 4a. by the
triangle inequality

Do not give this as an answer:  

   a     +    a    +   2a + b  =   4a + b

because it does not satisfy the triangle inequality.

Edwin