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S in any point on side QR of a Delta PQR...

S in any point on side QR of a `Delta PQR.Show that `PQ + QR+RP gt 2PS.`

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Given in `Delta PQR`,S is any point on side QR .

To show ` PQ +QR+RP gt 2 PS`
Proof In `Delta PQS. " " PQ + QS gt 2 PS " " ……(i)`
[sum of two sides of a triangle is grater then the third side ]
` Simiarly in " " SR+RP gt PS " "...(ii)`
[Sum of two sides of a triangle is greater then the third side ]
On adding Eqs.(i) and (ii) we get
` PQ +QS +SR+RP gt 2 PS`
`rArr " "PQ+(QS + SR) + RP gt 2 PS`
`rArr " "PQ+QR+RP gt 2 PS " " [because QR=QS + SR ]`
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S is any point on side QR of a DeltaPQR . Show that PQ+QR+RP gt 2PS .

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Knowledge Check

  • If S is any point on the side QR of a DeltaPQR , then

    A
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    B
    `PQ+QR+RP lt 2PS`
    C
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    D
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    C
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    D
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