Each midsegment is half the length of its corresponding parallel segment, so the perimeter of ∆MNK is half the perimeter of ∆ABC. Then the perimeter of ∆ABC is ...
... 2 × 5.2 in = 10.4 in
The side length ratios total 3+4+6 = 13 "ratio units" (corresponding to the total of side lengths, the perimeter), so the sides are 3/13, 4/13, and 6/13 of the perimeter, respectively. That is, the side lengths are ...
... 3/13 × 10.4 in = 2.4 in
... 4/13 × 10.4 in = 3.2 in
... 6/13 × 10.4 in = 4.8 in
