the most important concept here is all the triangles in the large triangle PQR are similar triangles which are all equilateral. upon drawing the smaller triangle of KLM, naturally, another 3 triangles which are exactly the same are formed. in terms of length, since the midpoint of the larger triangles sides are used vertices, the length is effectively halved (from k to 0.5k). as such, each time, the total perimeter is halved, making the common ratio 0.5.