Let the lengths of the legs be 







the perimeter is between 6 and 16 units





Multiply all three side by 2







Divide all three sides by 5:





The only integers  between 2.4 and 6.4, for
the legs are 



We aren't told that the base has to be an integer, 
too. If it had to be an integer too we would have to 
discard the odd integers for the legs.  But since we 
are not told that the base must be an integer, too,
we will stick with the above answer.

Edwin