Question

In Fig. T is a point on side QR of $\Delta PQR$ and S is a point such that RT = ST. Which of the following is true?

• A. PQ + PR < QS
• B. PQ + PR > QS
• C. PQ + TR > QS
• D. PQ + TR < QS

Answer 1

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 $\Delta PQR$, we have
PQ + PR > QR
PQ + PR > QT + RT
[Since QR = QT + RT]

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

In $\Delta QST$, we have
QT + ST > QS ..............(ii)

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