Question

In Fig. T is a point on side QR of △PQR and S is a point such that RT = ST. Prove that PQ + PR > QS

Answer 1

In $△$PQR, we have

PQ + PR $>$ QR

PQ + PR $>$ QT + RT [Since QR = QT+ RT]

PQ + PR$>$QT + ST .....(i)

In $△$QST, we have

QT + ST$>$QS ....(ii)

From (i) and (ii), we get

PQ + PR $>$ QS