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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?


  1. PQ + PR < QS

  2. PQ + PR > QS

  3. PQ + TR > QS

  4. 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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