Triangles ABC and LBM are similar. We know this because AL and LB have the same length, so that AB is twice as long as either AL or LB. The same goes for MC and BM, and BC. The angle B is the same for both tirangles ABC and LBM, so the side-angle-side postulate tells us the triangles are similar, and in particular that triangle ABC is twice as large as LBM.
All this to say that LM must be half as long as AC, so LM has length (B) 14 cm.
