In fig. 12.116 , T is a point on the side QR of ∆ PQR and S is a point such that RT=St.

Prove that PQ+PR>QS

Asked by shivendrasinghfauzdar | 9th Oct, 2021, 11:30: AM

Expert Answer:

As sum of two sides of a triangle is greater than the third side, we have
PQ + PR > QR
Therefore, PQ + QR > QT + TR   ... (As QR = QT + TR)
Therefore, PQ + QR > QT + TS   ... (As TR = TS) (1)
Also, in triangle QST, QT + TS > QS  ... (2) 
From (1) and (2), we have
PQ + QR > QS

Answered by Renu Varma | 23rd Oct, 2021, 07:15: PM