Answer:
x=11
Explanation:
If triangles QRS and TUV are similar, then the ratio of the corresponding sides are:
[tex]\frac{QR}{TU}=\frac{QS}{TV}=\frac{RS}{UV}[/tex]
Substituting the given lengths:
[tex]\begin{gathered} \frac{24}{x+5}=\frac{QS}{TV}=\frac{54}{36} \\ \implies\frac{24}{x+5}=\frac{54}{36} \end{gathered}[/tex]
We solve the equation above for x:
[tex]\begin{gathered} 54(x+5)=24\times36 \\ x+5=\frac{24\times36}{54} \\ x+5=16 \\ x=16-5 \\ x=11 \end{gathered}[/tex]
The value of x is 11.
