imc

Notice that we are given a parametric form of the region, and $w$ is used in both $x$ and $y$. We first fix $u$ and $v$ to $0$, and graph $(-3w,4w)$ from $0\le w\le 1$. When $w$ is $0$, we have the point $(0,0)$, and when $w$ is $1$, we have the point $(-3,4)$. We see that since this is a directly proportional function, we can just connect the dots like this: Now, when we vary $2u$ from $0$ to $2$, this line is translated to the right $2$ units: We know that any points in the region between the line (or rather segment) and its translation satisfy $w$ and $u$, so we shade in the region: We can also shift this quadrilateral one unit up, because of $v$. Thus, this is our figure: The length of the boundary is simply $1+2+5+1+2+5$ ($5$ can be obtained by Pythagorean theorem since we have side lengths $3$ and $4$.). This equals $\boxed{16}$