Answer:
[tex]z=\frac{15}{2}=7.5[/tex]
Step-by-step explanation:
If the two polygons are similar it means their corresponding angles are congruent and the measures of their corresponding sides are proportional.
If the sides are proportional we can construct a relationship between them like this:
[tex]\frac{AB}{EF}=\frac{AD}{EH}=\frac{BC}{FG}=\frac{DC}{HG}[/tex]
Using this relationships we can solve for z, more especifically if we use:
[tex]\frac{BC}{FG}=\frac{DC}{HG}[/tex]
where:
[tex]BC=8\\FG=6\\DC=10\\HG=z[/tex]
we replace the values:
[tex]\frac{8}{6}=\frac{10}{z}[/tex]
we solve for z
[tex]z=\frac{10*6}{8}\\z=\frac{15}{2}\\ z=7.5[/tex]
