question_answer

A soldier goes to a warfield and runs in the following manner. From the starting point, he goes West 25 m, then due North 60 m, then due East 80 m and finally due South 12 cm. The distance between the starting point and the finishing point is   

A)         177 m

B)  103 m        

C)  83 m   

D)  73 m   

Correct Answer: D

Solution :

 

Let P be the starting point of his run, then PT is the distance between the starting and the finishing point.

\[\therefore \]      \[PU=RQ-ST=60-12=48\,\,\text{m}\]

\[TU=RS-QP=80-25=55\,\,\text{m}\]

\[\therefore \]In \[\Delta PUT,\]\[P{{T}^{2}}={{(PU)}^{2}}+{{(TU)}^{2}}\]

\[\therefore \]      \[PT=\sqrt{{{(48)}^{2}}+{{(55)}^{2}}}=\sqrt{5329}=73\,\,\text{m}\]