In the adjoining figure, point S is any point on side QR of ∆PQR. P – InterviewSolution

InterviewSolution

1.

In the adjoining figure, point S is any point on side QR of ∆PQR. Prove that: PQ + QR + RP > 2PS

Answer»

In ∆PQS,

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

Similarly, in ∆PSR,

PR + SR > PS …(ii) [Sum of any two sides of a triangle is greater than the third side]

∴ PQ + QS + PR + SR > PS + PS

∴ PQ + QS + SR + PR > 2PS

∴ PQ + QR + PR > 2PS [Q-S-R]

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