Question

In the given figure, $\Delta OAB\sim \Delta OCD$. If $AB=8cm,BO=6.4cm,OC=3.5cm$ and $CD=5cm$, find
(i) $OA$
(ii) $DO$.

Answer 1

Since $\Delta OAB\sim \Delta OCD$

$AB=8cm,BO=6.4cmOC=3.5cm,CD=5cm$

Let $OD=y$ and $OA=x$

$\frac{AB}{CD}=\frac{OA}{OC}=\frac{BO}{DO}$

$\frac{8}{5}=\frac{x}{3.5}=\frac{BO}{DO}$

$\frac{x}{3.5}=\frac{8}{5}$

$\Rightarrow x=\frac{8\times 3.5}{5}=5.6$

and $\frac{6.4}{y}=\frac{8}{5}$

$\Rightarrow y=\frac{6.4\times 5}{8}=4.0$

$OA=5.6cm$ and $DO=4.0cm$