Question
In the given figure, $\angle\text{ABC}=90^\circ$ and $\text{BD}\perp\text{AC}.$ If BD = 8cm and AD = 4cm, find CD.
✓
Answer
In right $\triangle\text{ABC},$$\text{BD}\perp\text{AC}$
$\therefore\triangle\text{ABD}\sim\triangle\text{CBD}$
$\therefore\frac{\text{AD}}{\text{BD}}=\frac{\text{BD}}{\text{CD}}$
$\Rightarrow\frac{4}{8}=\frac{8}{\text{CD}}\Rightarrow\text{CD}=\frac{8\times8}{4}=16$
$\therefore\text{CD}=16\text{cm}$
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