Given that,
[tex]\Delta ABC\cong\Delta XYZ[/tex]
To solve for the length of the side XZ, we will apply the method of similar triangles.
Therefore,
[tex]\frac{AB}{AC}=\frac{XY}{XZ}[/tex]
Given data,
[tex]\begin{gathered} AB=2 \\ AC=3 \\ XY=7 \\ XZ=\text{?} \end{gathered}[/tex]
Let us now substitute the given data and solve for the length XZ,
[tex]\begin{gathered} \frac{2}{3}=\frac{7}{XZ} \\ \text{cross multiply,} \\ 2XZ=3\times7 \end{gathered}[/tex]
[tex]\begin{gathered} 2XZ=21 \\ \text{divide both sides by 2,} \\ \frac{2XZ}{2}=\frac{21}{2} \\ XZ=10.5 \end{gathered}[/tex]
Hence, the length of ZX is 10.5.
