# CBSE Class 9 Answered

**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 | 09 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 | 23 Oct, 2021, 07:15: PM

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