Question
In the given figure, $\triangle\text{OAB}\sim\triangle\text{OCD}.$ If $AB = 8\ cm, BO = 6.4\ cm$, $OC = 3.5\ cm$ and $CD = 5\ cm$, find.
- $OA$
- $DO$
✓
Answer
- Let OA be $x \ cm.$
$\therefore\frac{\text{OA}}{\text{OC}}=\frac{\text{AB}}{\text{CD}}$
$\Rightarrow\frac{\text{x}}{\text{3.5}}=\frac{\text{8}}{\text{5}}$ and
$\Rightarrow\text{x}=\frac{8\times3.5}{5}=5.6$
hence, $OA = 5.6\ cm$
- Let $OD$ be $y \ cm$
$\therefore\frac{\text{AB}}{\text{CD}}=\frac{\text{OB}}{\text{OD}}$
$\Rightarrow\frac{\text{8}}{\text{5}}=\frac{\text{6.4}}{\text{y}}$
$\Rightarrow\text{y}=\frac{6.4\times5}{8}=4$
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