Arithmetic sequence problem?

It is not a rectangular triangle, it is a right triangle. That means a^2 + b^2 = c^2 and the only combination with an arithmetic sequence is 3-4-5.

(1/2)ab = 60
a = 3k
b = 4k
(1/2) x 12 x k^2 = 60
k = √10
So the answer is 3√10, 4√10, and 5√10.