Question

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

Answer 1

In  triangle STR,

ST + TR > SR  …….(i)

In triangle PQT,

PQ + PT > QT  …..(ii)  

Adding (i) and (ii), we get

ST + TR  + PQ + PT > SR + QT

PQ + PR + ST > SR + QS + ST  (PT + TR = PR  and QT = QS + ST)

PQ + PR > SQ + SR    proved.

Answer 2

Step-by-step explanation:

In  triangle STR,

ST + TR > SR  …….(i)

In triangle PQT,

PQ + PT > QT  …..(ii)  

Adding (i) and (ii), we get

ST + TR  + PQ + PT > SR + QT

PQ + PR + ST > SR + QS + ST  (PT + TR = PR  and QT = QS + ST)

PQ + PR > SQ + SR    

Hence proved.