Answer:

The perimeter of the original rectangle is 12 cm.  The scale factor used in the dilation is 1.5. 

This means the perimeter of the new rectangle will be 1.5 times larger than the perimeter of the original, or 18 cm.

or

If the sides are multiplied by 1.5, the new dimensions will be 3 and 6.  This will result in a perimeter or 18 cm.