12. Determine the sides of a triangle if they are expressed as integers forming an arithmetic progression, and if the perimeter of the triangle is 15.
12. Let $a$ be the side of medium length in a triangle, the other two sides being $a-d$ and $a+d$. According to the problem, $3a=15, a=5$. The other two sides together amount to 10. We can construct a table of possible values for the sides.

The largest side of the triangle must be less than the sum of the other two sides. This condition is satisfied by the values in the first three columns of the table. Answer: The sides can have the following dimensions: $5,5,5$, $4,5,6$, and $3,5,7$.