Given that the triangles are similar, we can deduct that RS is proportional to UV, RQ is proportional to UT.
Having said that, we can form the following proportion.
[tex]\begin{gathered} \frac{RS}{UV}=\frac{RQ}{UT} \\ \frac{54}{36}=\frac{24}{x+5} \end{gathered}[/tex]
Then, we solve for x.
[tex]\begin{gathered} 54(x+5)=24\cdot36 \\ x+5=\frac{24\cdot36}{54} \\ x+5=\frac{864}{54} \\ x+5=16 \\ x=16-5 \\ x=11 \end{gathered}[/tex]Hence,
x is equal to 11.
