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# In PQR , Point S is on QR between Q and R, then the length

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Eternal Intern
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In PQR , Point S is on QR between Q and R, then the length [#permalink]

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16 Jul 2003, 17:52
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In PQR , Point S is on QR between Q and R, then the length of segment PS could be any number between?

PQ=9, QR=5, and PR=6.

I'm guessing PS is just a length.
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Joined: 23 Jun 2003
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16 Jul 2003, 18:46
PS is a line segment that splits triangle PQR into two: PQS and PRS.

Triangle PQS has two sides: 1) 9 and 2) 5 - x.
Triangle PRS has two sides: 2) 6 and 2) 5 - x.

PS has to be greater than 9 - (5-x) but less than 9 + (5+x)
PS has to be greater than 6 - (5-x) but less than 6 + (5 +x)
SVP
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16 Jul 2003, 23:02
Two extreme cases:

(1) the point S coincides with the point Q, so PQ=PS=9
(2) the point S coincides with the point R, so PR=PS=6

Thus, 6<PS<9
Eternal Intern
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17 Jul 2003, 09:08
I did Stolyar's way but I think JCohen's way is good too!

Welcome OnBoard AeroFlot and AirIndia JCohen!
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# In PQR , Point S is on QR between Q and R, then the length

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