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To solve this problem, we can set up a system of equations using the given information.

Let's represent AB as x and BC as y.

From the first equation, we have:

x + y = 17

From the second equation, we have:

x * y = 13.8 * 17

Now we can substitute the first equation into the second equation:

x * (17 - x) = 13.8 * 17

17x - x^2 = 234.6

Rearranging the equation:

x^2 - 17x + 234.6 = 0

Now we can solve this quadratic equation to find the values of x and y. The solutions are x = 13.8 and x = 3.8.

Therefore, the possible values for AB and BC are AB = 13.8 and BC = 3.2, or AB = 3.8 and BC = 13.2.