  Structural distortion in a three-leg-ladder is studied in connection with
Ludwigites, in particular the Fe and Co homometallic ones. Static impurities in
t_{2g}-orbitals as infinite repulsion potentials randomly located in the
three-leg-ladder and a Su-Schrieffer-Heeger like tight-binding Hamiltonian are
proposed and discussed. It is found that such potentials block itinerant
electrons and diminish a structural staggered order parameter, related with
structural distortion, as 3^{-M} being M the number of impurities. This
diminution is in detriment of Peierls like distortion that occurs in these
ladders as in the case of Fe-Ludwigite. On the other hand, this diminution
could explain the lack of structural distortion as in the case of Co-Ludwigite.
