請幫手解決呢條arithmetic sequence 問題

As a, b, c are in arithmetic sequence,
let a = k-m, b = k and c = k+m.
(k-m)^2 + k^2 = (k+m)^2
2k^2 - 2km + m^2 = k^2 + 2km + m^2
k^2 - 4km = 0
k(k-4m) = 0
k = 0 or 4m
The answer k = 0 is rejected because it is impossible for a side of triangle is 0.
Therefore, k = 4m
a = 4m - m = 3m, b = 4m and c = 5m
Therefore a:b:c = 3m:4m:5m = 3:4:5