question_answer

In the given figure, ABCD is a rectangle in which segments AP and AQ are drawn as shown. Then the length of \[(AP+AQ)\]is  '

A)  300 cm          

B)  350 cm          

C)  320 cm       

D)  360 cm                      

Correct Answer: A

Solution :

In rt. \[\Delta \,ADQ,\frac{AD}{AQ}=\sin {{30}^{o}}\Rightarrow \frac{AD}{AQ}=\frac{1}{2}\] \[\Rightarrow \] \[AQ=2AD\Rightarrow AQ=2\times 60=120cm.\]                                                 ?.(1)             In rt. \[\Delta \,ABP,\frac{AB}{AP}=\cos {{60}^{o}}\Rightarrow \frac{AB}{AP}=\frac{1}{2}\] \[\Rightarrow \]            \[AP=2AB\] \[\Rightarrow \]            \[AP=2\times 90\]\[=180\,cm\]     ?.(2) \[\therefore \]    \[AP+AQ\] \[=120+180\] \[=300\,cm.\] [From (1) and (2)]