Question

7. In Fig. 10.42, T is a point in the exterior of APQR. Show that
PQ + QR + PR < 2 (TP + TQ + TR)​

Answer 1

Step 1:

Given Data: PQR is triangle on side QR T is a point.

To Calculate the PQ + PR >QS

Step 2:

In triangle PQR, we have,

PQ + PR > QR  

Step 3:

PQ + PR > QT + TR [AS, QR = QT + TR]

PQ + PR > QT + TS [as, TR = TS]  ..................................(1)

Step 4:

In triangle QST, we have,

QT + TS  > QS  ……………………………………(2)

Step 5:  

Equation (1) and Equation (2), we calculate that,

PQ + PR > QS

Hence it is proved