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Mathematics · 2023 · 2 marks
CBSE 2023 · Region 1 · Set 1 · Q22
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.
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.
Marking-scheme solution
As \(\displaystyle X Z \| B C\) Therefore \(\displaystyle \frac{A X}{X B}=\frac{3}{2}=\frac{A Z}{Z C}\) - (i)
\[\begin{aligned}
& \Delta \mathrm{AXY} \sim \Delta \mathrm{ABM} \\
& \Rightarrow \frac{A X}{A B}=\frac{X Y}{B M} \text { or } \frac{3}{5}=\frac{X Y}{3} \\
& \Rightarrow X Y=\frac{9}{5} \text { or } 1 \cdot 8 \mathrm{~cm}
\end{aligned}
\]
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CBSE Class 10 Mathematics past-paper question from the 2023 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.