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Mathematics · 2026 · 2 marks
CBSE 2026 · Region 1 · Set 1 · Q22
In $\displaystyle \Delta \mathrm{ABC}, \mathrm{DE} \| \mathrm{BC}$. If $\displaystyle \mathrm{AD}=x, \mathrm{DB}=x-2, \mathrm{AE}=x+2$ and $\displaystyle \mathrm{EC}=x-1$, then find the value of $\displaystyle x$.
In the figure given above, $\displaystyle \Delta \mathrm{ABC} \sim \Delta \mathrm{XYZ}$, then find the values of $\displaystyle x$ and $\displaystyle y$.
In $\displaystyle \Delta \mathrm{ABC}, \mathrm{DE} \| \mathrm{BC}$. If $\displaystyle \mathrm{AD}=x, \mathrm{DB}=x-2, \mathrm{AE}=x+2$ and $\displaystyle \mathrm{EC}=x-1$, then find the value of $\displaystyle x$.
In the figure given above, $\displaystyle \Delta \mathrm{ABC} \sim \Delta \mathrm{XYZ}$, then find the values of $\displaystyle x$ and $\displaystyle y$.
Marking-scheme solution
Since \(\displaystyle \mathrm{DE} \| \mathrm{BC} \Rightarrow \frac{\mathrm{AD}}{\mathrm{DB}}=\frac{\mathrm{AE}}{\mathrm{EC}}\)
\[\Rightarrow \frac{x}{x-2}=\frac{x+2}{x-1}
\]
Solving, we get \(\displaystyle x=4\)
\[\begin{aligned}
& \Delta \mathrm{ABC} \sim \Delta \mathrm{XYZ} \Rightarrow \frac{\mathrm{AB}}{\mathrm{XY}}=\frac{\mathrm{BC}}{\mathrm{YZ}}=\frac{\mathrm{AC}}{\mathrm{XZ}} \\
& \Rightarrow \frac{4}{x}=\frac{6}{7.2}=\frac{y}{6}
\end{aligned}
\]
Solving, we get \(\displaystyle x=4.8 \mathrm{~cm}, y=5 \mathrm{~cm}\)
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CBSE Class 10 Mathematics past-paper question from the 2026board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.