Question

In the given figure $∆OAB~∆OCD.\mathrm{If}AB=8\mathrm{cm},BO=6.4\mathrm{cm},OC=3.5\mathrm{and}CD=5\mathrm{cm},$ Find
(i) OA
(ii) DO.

Answer 1

(i) Let OA be x cm.
$\because$ $△OAB~△OCD$
$$\begin{gathered} \therefore \frac{OA}{OC}=\frac{AB}{CD} \\ \Rightarrow \frac{x}{3.5}=\frac{8}{5} \\ \Rightarrow x=\frac{8\times 3.5}{5}=5.6 \end{gathered}$$
Hence, OA = 5.6 cm

(ii) Let OD be y cm

$\because$ $△OAB~△OCD$
$$\begin{gathered} \therefore \frac{AB}{CD}=\frac{OB}{OD} \\ \Rightarrow \frac{8}{5}=\frac{6.4}{y} \\ \Rightarrow y=\frac{6.4\times 5}{8}=4 \end{gathered}$$
Hence, DO = 4 cm