question_answer

If S is any point on the side QR of a\[\Delta PQR,\]  then

A)  PQ+ QR+ RP > 2PS

B)         PQ+QR+ RP< 2PS

C)         PQ + QR + RP = 3PS

D)         None of these

Correct Answer: A

Solution :

In \[\Delta PQS,\]we have \[PQ+QS>PS\]                                      ?(i) [\[\therefore \]Sum of two sides of a \[\Delta \]is greater than the third side] Similarly, in\[\Delta PRS,\]we have \[RP+RS>PS\]                           ?(ii) Adding (i) and (ii), we get \[(PQ+QS)+(RP+RS)>PS+PS\] \[\Rightarrow \]\[PQ+(QS+RS)+RP>2PS\] \[\Rightarrow \]\[PQ+QR+RP>2PS\]\[[\because \,QS+RS=QR]\]