Answer: [tex]3\sqrt{10}[/tex]
Step-by-step explanation:
By the geometric mean theorem,
[tex]\frac{y}{3}=\frac{27}{y}\\y^{2}=81\\y=9[/tex]
So, by the Pythagorean theorem,
[tex]3^{2}+9^{2}=z^{2}\\90=z^{2}\\z=\boxed{3\sqrt{10}}[/tex]
