Let the sides be ( a-d,\ a,\ a+d ) (in A.P.) with ( a+d ) the hypotenuse (largest side).
By Pythagoras: [ (a-d)^2 + a^2 = (a+d)^2 ] [ a^2 - 2ad + d^2 + a^2 = a^2 + 2ad + d^2 ] [ 2a^2 - 2ad = a^2 + 2ad ] [ a^2 - 4ad = 0 ] [ a(a - 4d) = 0 ]
Since ( a \ne 0 ), ( a = 4d )
Sides: ( 4d - d = 3d ), ( 4d ), ( 4d + d = 5d )
Ratio: ( 3 : 4 : 5 )
Answer: ( 3 : 4 : 5 )