In the given figure, XZ is parallel to BC. $\displaystyle \mathrm{AZ}=3 \mathrm{~cm}, \mathrm{ZC}=2 \mathrm{~cm}, \mathrm{BM}=3 \mathrm{~cm}$ and $\displaystyle \mathrm{MC}=5 \mathrm{~cm}$. Find the length of XY.

As \(\displaystyle X Z \| B C\) Therefore \(\displaystyle \frac{A X}{X B}=\frac{3}{2}=\frac{A Z}{Z C}\) - (i) \[\begin{aligned} & \Delta \mathrm{AXY} \sim \Delta \mathrm{ABM} \\ & \Rightarrow \frac{A X}{A B}=\frac{X Y}{B M} \text { or } \frac{3}{5}=\frac{X Y}{3} \\ & \Rightarrow X Y=\frac{9}{5} \text { or } 1 \cdot 8 \mathrm{~cm} \end{aligned} \]