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Mathematics · 2024 · 2 marks
CBSE 2024 · Region 1 · Set 3 · Q25
In ABC, altitudes AD and BE are drawn. If AD =7 cm, BE =9 cm and EC =12 cm then, find the length of CD.
In $\displaystyle \triangle \mathrm{ABC}$, altitudes AD and BE are drawn. If $\displaystyle \mathrm{AD}=7 \mathrm{~cm}$, $\displaystyle \mathrm{BE}=9 \mathrm{~cm}$ and $\displaystyle \mathrm{EC}=12 \mathrm{~cm}$ then, find the length of CD.
Marking-scheme solution
\[\begin{aligned}
& \triangle \mathrm{BEC} \sim \triangle \mathrm{ADC} \\
& \Rightarrow \frac{B E}{A D}=\frac{E C}{C D} \\
& \Rightarrow C D=\frac{12 \times 7}{9}=\frac{28}{3} \text { or } 9.33 \mathrm{~cm}
\end{aligned}
\]
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