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Mathematics · 2024 · 2 marks
CBSE 2024 · Region 4 · Set 1 · Q25
In the given figure, Δ AHK ∼ Δ ABC. If AK =8 cm, BC =3 · 2 cm and HK =6 · 4 cm, then find the length of AC.
In the given figure, $\displaystyle \Delta \mathrm{AHK} \sim \Delta \mathrm{ABC}$. If $\displaystyle \mathrm{AK}=8 \mathrm{~cm}, \mathrm{BC}=3 \cdot 2 \mathrm{~cm}$ and $\displaystyle \mathrm{HK}=6 \cdot 4 \mathrm{~cm}$, then find the length of AC.
Marking-scheme solution
\[\begin{aligned}
& \because \triangle \mathrm{AHK} \sim \triangle \mathrm{ABC} \text { (given) } \\
& \therefore \frac{H K}{B C}=\frac{A K}{A C} \\
& \Rightarrow \frac{6.4}{3.2}=\frac{8.0}{A C} \\
& \Rightarrow \mathrm{AC}=4 \mathrm{~cm}
\end{aligned}
\]
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