Solution:
Given:
Since triangle TUS and triangle TVW are similar, then the ratios of corresponding sides are in proportion.
Hence,
[tex]\begin{gathered} \frac{y}{6}=\frac{27}{54} \\ \frac{y}{6}=\frac{1}{2} \\ Cross\text{ multiplying;} \\ 2y=6 \\ y=\frac{6}{2} \\ y=3 \end{gathered}[/tex]Also,
[tex]\begin{gathered} \frac{4}{6}=\frac{x}{54} \\ Cross\text{ multiplying;} \\ 6x=4\times54 \\ 6x=216 \\ x=\frac{216}{6} \\ x=36 \end{gathered}[/tex]Therefore,
x = 36
y = 3
