Solution:
According to the given question,
![\[XY\text{ }||\text{ }BC\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-ee1728dfb6e620164d40ac568f1ae249_l3.png "Rendered by QuickLaTeX.com")
So, In
![\[\Delta \text{ }AXY\text{ }and\text{ }\Delta \text{ }ABC\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-ce22d2d6f667464848a9a98d5af816a7_l3.png "Rendered by QuickLaTeX.com")
![\[\angle AXY\text{ }=\angle ABC\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-f3d6bdce56ed528c2099eec17ede0d82_l3.png "Rendered by QuickLaTeX.com")
[Corresponding angles]
![\[\angle AYX\text{ }=\angle ACB\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-22c2c10b2ec5de04850f2356cdc69827_l3.png "Rendered by QuickLaTeX.com")
[Corresponding angles]
Hence,
![\[\vartriangle AXY\text{ }\sim\text{ }\vartriangle ABC\text{ }by\text{ }AA\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-4ce40c0ccaaefde8c3b17f5bebf9b01a_l3.png "Rendered by QuickLaTeX.com")
criterion for similarity.
As corresponding sides of similar triangles are proportional, we have
As,
![\[\vartriangle AXY\text{ }\sim\text{ }\vartriangle ABC\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-d9d77e739d7c2b58a6eded0143719b7d_l3.png "Rendered by QuickLaTeX.com")
![\[AX/AB\text{ }=\text{ }XY/BC\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-a61d0de3a7eda73b8e09064ca29de2ee_l3.png "Rendered by QuickLaTeX.com")
![\[9/13.5\text{ }=\text{ }XY/18\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-3fec81925b5977c9a5214ed0d84a77c0_l3.png "Rendered by QuickLaTeX.com")
Or,
![\[XY\text{ }=\text{ }\left( 9\text{ }x\text{ }18 \right)/\text{ }13.5\text{ }=\text{ }12\text{ }cm\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-9e445afa5e01bee5b6300a8fddcac956_l3.png "Rendered by QuickLaTeX.com")
