CBSE 2025 · Region 6 · Set 3 · Q23 · 2 marks
In the adjoining figure, $\displaystyle \mathrm{AP}=1 \mathrm{~cm}, \mathrm{BP}=2 \mathrm{~cm}, \mathrm{AQ}=1.5 \mathrm{~cm}$ and $\displaystyle \mathrm{AC}=4.5 \mathrm{~cm}$.
Prove that $\displaystyle \triangle \mathrm{APQ} \sim \triangle \mathrm{ABC}$. Hence find the length of PQ , if $\displaystyle \mathrm{BC}=3.6 \mathrm{~cm}$.
Prove that $\displaystyle \triangle \mathrm{APQ} \sim \triangle \mathrm{ABC}$. Hence find the length of PQ , if $\displaystyle \mathrm{BC}=3.6 \mathrm{~cm}$.Marking-scheme solution
\(\displaystyle \frac{\mathrm{AP}}{\mathrm{AB}}=\frac{1}{3} ; \frac{\mathrm{AQ}}{\mathrm{AC}}=\frac{1.5}{4.5}=\frac{1}{3}\)
\(\displaystyle \angle \mathrm{ACP}=\angle \mathrm{ACB}\)
\(\displaystyle \Delta \mathrm{APQ} \sim \triangle \mathrm{ABC}\)
\(\displaystyle \mathrm{PQ}=1.2 \mathrm{~cm}\)
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