#### Answer

$m=45$ and $n=60$

#### Work Step by Step

Similar triangles have corresponding sides in proportion.
Side of length 75 corresponds to side of length 50 and side of length n corresponds to side of length 40.
This leads to the following proportion:
$\frac{75}{50}=\frac{n}{40}$
Solving, $75\times40=50\times n$
$3000=50n$
Dividing both sides by $50, $$n=60$.
Side of length 75 corresponds to side of length 50 and side of length m corresponds to side of length 30.
This leads to the following proportion:
$\frac{75}{50}=\frac{m}{30}$
Solving, $75\times30=50\times m$
$2250=50m$
Dividing both sides by $50, $$m=45$.