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PQR is a triangle. S is a point on the s...

PQR is a triangle. S is a point on the side QR of `DeltaPQR ` such that `/_PSR = /_QPR`. Given QP = 8 cm, PR = 6 cm and SR = 3 cm.

Find the lengths of QR and PS.

Text Solution

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Given : A point S on side QR of `DeltaPQR`.
Tp prove : `PQ+QR+RP gt 2PS`
Proof : In `DeltaPQS`, we have
`PQ+QS gt PS` ...(1)
( `:'` sum of any sides of a triangle is greater than the third side)
Now, in `DeltaPSR`, we have
`RS+RP gt PS` ...(2)
( `:'` Sum of any two sides of a triangle is greater than the third side)
Adding (1) and (2), we get
`PQ+QS+RS+RP gt 2PS`
`implies PQ+QR+RP gt 2PS`
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