these two polygons are similar. z = ?

Explanation:

Step1: Find the scale - factor

The ratio of corresponding sides of similar polygons is the same. Let's find the scale - factor using the known corresponding sides. Consider the sides of length 3 and 15. The scale - factor $k$ is $\frac{15}{3}=5$.

Step2: Solve for $z$

Since the scale - factor is 5 and the side corresponding to $z$ has length 9, we can set up the proportion $\frac{z}{9}=\frac{3}{15}$. Cross - multiplying gives $15z = 3\times9$. Then $z=\frac{3\times9}{15}=\frac{27}{15}=\frac{9}{5} = 1.8$. Another way is to use the scale - factor. If the scale - factor from the small polygon to the large polygon is 5, then $z=\frac{9}{5}=1.8$.

Answer:

$1.8$