Question 118100
Ideas to consider.
1.Each of the three sides must be 1 or 2 or 3 ... or 7
2.There are 7*7*7 = 343 such patterns of side lengths.
3.Only those patterns where the sum of each pair of sides
is greater than the third side will form a triangle. 
For example 1,2,7 cannot form a triangle.
4. Getting started
Let one side be 7 and figure out what the other sides must
be: 
(7,1,7)-----no others starting with (7,1
(7,2,7),(7,2,6) ----no others starting with (7,2
(7,3,7),(7,3,6),(7,3,5)---no others starting with (7,3
etc.
Follow some pattern of development, without duplicating, till you
have all the possible patterns listed.
==============
Cheers,
Stan H.