Find two similar triangles with sides (A,B,C) and (A,B,D), such that D-C=20141.

(In reply to

Almost there... by Federico Kereki)

Actually R does not need to be an integer, R being a rational would suffice. Let R=N/D where N and D are integers. Then the equation C(R³-1)=11*1831 becomes C(N³-D³)=D³*11*1831. N=30 and D=19 is a solution to the latter equation. Then C=6859, A=10830, B=17100, D=27000 and R=30/19.