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Question

In fig(iv), T is a point on side QR of triangle PQR and S is a point such that RT = ST. Prove that PQ + PR > QS
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Solution

In PQR,PQ+PR>QR sum of the two sides is greater than the third side.
PQ+PR>QT+TR QR=QT+TR
PQ+PR>QT+TS .....(1) TR=TS
In QST,QT+TS>QS .....(2)
from (1) and (2) we have
PQ+PR>QS
Hence proved

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