Answer
$x=12$ mm
$y=7.5$ mm
Perimeter: 38 mm
Work Step by Step
To solve for side $x$, we set up a proportion with corresponding sides:
$\displaystyle \frac{16}{12}=\frac{x}{9}$
Cross-multiply:
$16*9=12x$
$12x=144$
$x=144/12$
$x=12$ mm
Similarly, we set up another proportion to solve for $y$:
$\displaystyle \frac{16}{12}=\frac{10}{y}$
Cross-multiply:
$16y=10*12$
$16y=120$
$y=120/16$
$y=7.5$ mm
Finally, we find the perimeter of the large triangle:
$12+10+16=38$ mm