Question

# In Fig. T is a point on side QR of ΔPQR and S is a point such that RT = ST. Which of the following is true? PQ + PR < QS PQ + PR > QS PQ + TR > QS PQ + TR < QS

Solution

## The correct option is B PQ + PR > QS Sum of the lengths of the two sides is always greater than the length of third side. So in ΔPQR, we have PQ + PR > QR PQ + PR > QT + RT                    [Since QR = QT + RT] PQ + PR > QT + ST  ............. (i)                      [Since RT =  ST] In ΔQST, we have QT + ST > QS    ..............(ii) From (i) and (ii), we get PQ + PR > QS

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