The triangles are similar; therefore, the corresponding sides are proportional. They divide to form the same ratio
(larger horizontal side)/(smaller horizontal side) = 12/9
(larger vertical)/(smaller vertical) = 16/y
The two fractions are equal to one another as they divide to get the same ratio, so,
12/9 = 16/y
12y = 9*16 .... cross multiply
12y = 144
y = 144/12 .... divide both sides by 12
y = 12 which is the answer we want
