Question
In the given figure, $\angle\text{ABC}=90^\circ$ and $\text{BD}\perp\text{AC}.$ If BD = 8cm, AD = 4cm, find CD.
✓
Answer
Given that BD = 8cm, AD = 4cmIn $\triangle\text{DBA}$ and $\triangle\text{DCB},$ we have
$\angle\text{BDA}=\angle\text{CDB}=90^\circ$
$\angle\text{DBA}=\angle\text{DCB}$ $\big[\text{each}=90^\circ-\angle\text{A}\big]$
$\therefore\triangle\text{DBA}\sim\triangle\text{DCB}$ (by AAA similaritiy)
$\therefore\frac{\text{BD}}{\text{CD}}=\frac{\text{AD}}{\text{BD}}$
$\Rightarrow\text{CD}=\frac{\text{BD}^2}{\text{AD}}$
$\Rightarrow\text{CD}=\frac{(\text{8)}^2}{\text{4}}=\frac{64}{4}=16\text{cm}$
Hence, CD= 16cm
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