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S is any point on side QR of triangle PQR. Prove that :

PQ + QR + RP > 2PS

S is any point on side QR of triangle PQR. Prove that : Inequalities, Concise Mathematics Solutions ICSE Class 9.

Triangles

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Answer

In △ PQS,

⇒ PQ + QS > PS ……..(1) [Sum of any two sides of a triangle is greater than the third side]

In △ PRS,

⇒ RP + RS > PS ……..(2) [Sum of any two sides of a triangle is greater than the third side]

Adding equations (1) and (2), we get :

⇒ PQ + QS + RP + RS > PS + PS

⇒ PQ + (QS + RS) + RP > 2PS

⇒ PQ + QR + RP > 2PS.

Hence, proved that PQ + QR + RP > 2PS.

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