#### Answer

$p=q=7$

#### Work Step by Step

Similar triangles have corresponding sides in proportion.
Side of length 16 corresponds to side of length 7 and side of length 16 corresponds to side of length p.
This leads to the following proportion:
$\frac{16}{7}=\frac{16}{p}$
Solving, $16\times7=16\times p$
$112=16p$
Dividing both sides by $16, $$p=7$.
Side of length 16 corresponds to side of length 7 and side of length 16 corresponds to side of length q.
This leads to the following proportion:
$\frac{16}{7}=\frac{16}{q}$
Solving, $16\times7=16\times q$
$112=16q$
Dividing both sides by $16, $$q=7$.