The big triangle and the smallest triangle are similar, then:
[tex]\frac{z}{27+3}=\frac{3}{z}\text{.}[/tex]
Solving the above equation for z, we get:
[tex]\begin{gathered} \frac{z^2}{30}=3, \\ z^2=90, \\ z=\sqrt[]{90}. \end{gathered}[/tex]
Answer:
[tex]z=3\sqrt[]{10}.[/tex]
