Answer:
t = 6.5
Explanation:
Since triangle ABC and triangle XYZ are similar, the ratio of the corresponding sides is constant.
Then, AB and XY are corresponding and AC and XZ are corresponding, so
[tex]\begin{gathered} \frac{AB}{XY}=\frac{AC}{XZ} \\ \frac{19.5}{t}=\frac{13.5}{4.5} \end{gathered}[/tex]
To solve for t, we need to cross multiply, so
[tex]\begin{gathered} 19.5(4.5)=13.5t \\ 87.75=13.5t \end{gathered}[/tex]
Divide both sides by 13.5
[tex]\begin{gathered} \frac{87.75}{13.5}=\frac{13.5t}{13.5} \\ 6.5=t \end{gathered}[/tex]
Therefore, t = 6.5
