Question 133099
Let the shortest side = s. Then the hypotenuse is (s+6) and the other side is (s+6)-3 = (s+3)

Using the Pythagorean theorem, {{{s^2 + (s+3)^2 = (s+6)^2}}}
So:
{{{s^2 + s^2+6s +9 = s^2 + 12s +36}}}
collecting terms yields:
{{{s^2 -6s -27 = 0 }}}
{{{(s-9)(s+3) = 0 }}}

Thus s = 9 (since it can't be a length of -3)
Then the other 2 kegs are (s+3) = 12   and (s+6) = 15

Check your answer.
Is 9^2 + 12^2 = 15^2? yes it is!