In Fig. T is a point on side QR of $Δ P Q R$ and S is a point such that RT = ST. Which of the following is true?

PQ + PR < QS

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PQ + PR > QS

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PQ + TR > QS

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PQ + TR < QS

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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 $Δ P Q R$ , we have
PQ + PR > QR
PQ + PR > QT + RT
[Since QR = QT + RT]

PQ + PR > QT + ST ............. (i)
[Since RT = ST]

In $Δ Q S T$ , we have
QT + ST > QS ..............(ii)

From (i) and (ii), we get
PQ + PR > QS

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In the given figure, T is a point on side QR of $Δ P Q R$ and S is a point such that RT = ST.
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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

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In the given figure, RS = QT and QS = RT. Then which of the following options is correct?

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