jmc

The large triangle $ABC$ has sides of length $4$. The medium triangle has sides of length $2$. The small triangle has sides of length $1$. There are $3$ segment sizes, and all segments depicted are one of these lengths. Starting at $A$ and going clockwise, the perimeter is: $AB+BC+CD+DE+EF+FG+GA$ $4+4+2+2+1+1+1$ $15$, thus the answer is $\boxed{15}$