Answer: The required value of z is 7.5.
Step-by-step explanation: We are given that the polygons shown in the figure are similar.
We are to find the value of z.
From the figure, we see two quadrilaterals ABCD and EFGH with corresponding sides as follows :
(AB, EF), (BC, FG), (CD, GH) and (DA, HE).
Since the corresponding sides of two similar figures are proportional, so we must have
[tex]\dfrac{AB}{EF}=\dfrac{BC}{FG}=\dfrac{CD}{GH}=\dfrac{DA}{HE}\\\\\\\Rightarrow \dfrac{6}{y}=\dfrac{8}{6}=\dfrac{10}{z}=\dfrac{x}{12}\\\\\\\Rightarrow \dfrac{8}{6}=\dfrac{10}{z}\\\\\\\Rightarrow z=\dfrac{10\imes6}{8}\\\\\Rightarrow z=7.5.[/tex]
Thus, the required value of z is 7.5.
