Given data:
The given triangle is shown.
In traingle XWY and triangle ZWY, the ratio of the corresponding sides is,
[tex]\frac{XW}{ZW}=\frac{XY}{ZY}[/tex]
Substitute the given values in the above expression.
[tex]\begin{gathered} \frac{15}{21}=\frac{XY}{ZY} \\ \frac{5}{7}=\frac{XY}{YZ} \\ \frac{YZ}{XY}=\frac{7}{5} \\ YZ=\frac{7}{5}XY \end{gathered}[/tex]
The XZ length is,
[tex]\begin{gathered} XZ=XY+YZ \\ 24=XY+\frac{7}{5}XY \\ 24=\frac{12}{5}XY \\ XY=10 \end{gathered}[/tex]
Thus, the XY length is 10 units.
