In the given figure $QA\text{and}PB$  are perpendicular to $AB$ . If $AO=8\text{cm}\text{,}BO=10\text{cm},PB=18\text{cm},$  then $QA=$

In $\Delta QAO$  and $\Delta PBO$

$\angle A=\angle B\left[\because \text{Right angle}\right]$

$\angle AOQ=\angle BOP\left[\because \text{Vertically opposite angles}\right]$

So, by $A.A$  similarly

$\Delta QAO\sim \Delta PBO$

$\therefore \frac{QA}{PB}=\frac{AO}{BO}$

$\Rightarrow \frac{QA}{18}=\frac{8}{10}$

$\Rightarrow QA=\frac{18\times 4}{5}$

$\Rightarrow QA=14.4$