Question

In the given figure, PQR is a triangle and S is any point in its interior. Show that $SQ+SR<PQ+PR$.

Answer 1

Produce $QS$ meet $PR$ at $T$

In triangle $PQT$

$PQ+PT>QT$

$QT=QS+ST$

$PQ + PT>QS+ST$ .......(1)

In triangle $STR$

$TR+ST>RS$.......(2)

Adding equation (1) and (2)

$PQ+PT+TR+ST>QS+ST+RS$

$PQ+PR+ST>QS+ST+RS$

$PQ+PR>QS+RS$