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

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Question

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

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Accepted Answer

Step 1: As $XZ \parallel BC$, therefore $\frac{AX}{XB} = \frac{3}{2} = \frac{AZ}{ZC}$ ... (i)
Step 2: $	riangle AXY \sim 	riangle ABM$
Step 3: $\Rightarrow \frac{AX}{AB} = \frac{XY}{BM}$ or $\frac{3}{5} = \frac{XY}{3}$
Step 4: $\Rightarrow XY = \frac{9}{5}$ or $1.8$ cm

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