Given that the triangles are similar, then their corresponding sides are in proportion, that is,
[tex]\frac{XY}{AB}=\frac{YZ}{BC}[/tex]Substituting with data:
[tex]\begin{gathered} \frac{40\text{ ft}}{10\text{ ft}}=\frac{YZ}{10\text{ ft}} \\ 40\cdot10=YZ\cdot10 \\ \frac{400}{10}=YZ \\ 40\text{ ft = YZ} \end{gathered}[/tex]