If the smallest side were 1, then the other sides would have to add
to 8.  They couldn't be 4 and 4 because the triangle would be isosceles,
not scalene. They couldn't be 3 and 5, because then the sum of the
smaller two sides would be 1 + 3 which would be less then the third side
5.  And they sure couldn't be 2 and 6, because then the sum of the
smaller two sides would be 1 + 2 which would be less then the third side
6.  So the smallest side cannot be 1.

If the smallest side is 2, then the other two sides whould have to
add to 7, and they could only be 3 and 4.

So there is only one scalene triangle with perimeter 9 units, and each 
side being a whole number of units in length, 2 units, 3 units, and 4 
units.  It looks like this:


 
Edwin