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Mathematics · 2026 · 2 marks
CBSE 2026 · Region 2 · Set 2 · Q21
In the given figure, $\displaystyle \Delta \mathrm{AHK} \sim \Delta \mathrm{ABC}$. If $\displaystyle \mathrm{AK}=10 \mathrm{~cm}, \mathrm{BC}=3 \cdot 5 \mathrm{~cm}$ and $\displaystyle \mathrm{HK}=7 \mathrm{~cm}$, find the length of AC .
In the given figure, $\displaystyle \mathrm{XY} \| \mathrm{QR}, \frac{\mathrm{PQ}}{\mathrm{XQ}}=\frac{7}{3}$ and $\displaystyle \mathrm{PR}=6 \cdot 3 \mathrm{~cm}$. Find the length of YR.
In the given figure, $\displaystyle \Delta \mathrm{AHK} \sim \Delta \mathrm{ABC}$. If $\displaystyle \mathrm{AK}=10 \mathrm{~cm}, \mathrm{BC}=3 \cdot 5 \mathrm{~cm}$ and $\displaystyle \mathrm{HK}=7 \mathrm{~cm}$, find the length of AC .
In the given figure, $\displaystyle \mathrm{XY} \| \mathrm{QR}, \frac{\mathrm{PQ}}{\mathrm{XQ}}=\frac{7}{3}$ and $\displaystyle \mathrm{PR}=6 \cdot 3 \mathrm{~cm}$. Find the length of YR.
Marking-scheme solution
\(\displaystyle \Delta \mathrm{AHK} \sim \Delta \mathrm{ABC}\)
\(\displaystyle \frac{A K}{A C}=\frac{H K}{B C}\)
\(\displaystyle \Rightarrow \frac{10}{A C}=\frac{7}{3.5}\)
\(\displaystyle \Rightarrow \mathrm{AC}=5 \mathrm{~cm}\)
XY||QR
\(\displaystyle \frac{\mathrm{PQ}}{\mathrm{XQ}}=\frac{\mathrm{PR}}{\mathrm{YR}}\)
\(\displaystyle \Rightarrow \frac{7}{3}=\frac{6.3}{\text { YR }}\)
\(\displaystyle \Rightarrow \mathrm{YR}=2.7 \mathrm{~cm}\)
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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.