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# In the figure, if QS=6 units and PS=8 units, then what is the length

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Intern
Joined: 30 Aug 2017
Posts: 15
In the figure, if QS=6 units and PS=8 units, then what is the length [#permalink]

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07 Oct 2017, 10:23
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In the figure, if QS=6 units and PS=8 units, then what is the length of segment SR ?

I don't have options. The answer is= 32/3.
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Manager
Joined: 13 Apr 2016
Posts: 62
WE: Information Technology (Retail Banking)
Re: In the figure, if QS=6 units and PS=8 units, then what is the length [#permalink]

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07 Oct 2017, 12:02
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KUDOS
In the figure, if QS=6 units and PS=8 units, then what is the length of segment SR ?

I don't have options. The answer is= 32/3.

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Intern
Joined: 28 Dec 2010
Posts: 49
Re: In the figure, if QS=6 units and PS=8 units, then what is the length [#permalink]

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08 Oct 2017, 02:45
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It would be very simple if you use similar triangle property.

So Triangle PQS ~ Triangle RPS

$$\frac{PS}{QS} = \frac{RS}{PS}$$

$$RS = \frac{PS * PS}{QS}$$

RS = 64/6
= 32/3
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Intern
Joined: 20 Aug 2016
Posts: 23
GMAT 1: 570 Q46 V23
WE: Information Technology (Other)
Re: In the figure, if QS=6 units and PS=8 units, then what is the length [#permalink]

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08 Oct 2017, 03:20
triangle RPQ is similar to trainagle PSQ =>PQ/QR = QS/PQ.
by Pythagoras theorem, PQ = 10.
=> 100/6 = QR
=> QR = 50/3 => QS+SR = 50/3
=> SR = 50/3 - 6/1
=>SR = 32/3
Intern
Joined: 09 Oct 2017
Posts: 1
Re: In the figure, if QS=6 units and PS=8 units, then what is the length [#permalink]

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09 Oct 2017, 20:38
Given that only both are right triangles and only one side PR is common, then how did you apply similar triangles rules , please explain

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Manager
Joined: 24 Jun 2017
Posts: 118
Re: In the figure, if QS=6 units and PS=8 units, then what is the length [#permalink]

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09 Oct 2017, 21:05
Just playing with algebra a little bit (ignore negative value)
24+4x=5(sq64+x^2)
16x^2+576=1600+25x^2
9x^2=-1024
3x=32
x=32/3
Director
Joined: 13 Mar 2017
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Location: India
Concentration: General Management, Entrepreneurship
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Re: In the figure, if QS=6 units and PS=8 units, then what is the length [#permalink]

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10 Oct 2017, 01:35
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KUDOS
In the figure, if QS=6 units and PS=8 units, then what is the length of segment SR ?

I don't have options. The answer is= 32/3.

For a right angles triangle as given in figure always remember
PS^2 = QS * SR
8^2 = 6 * SR
SR = 64/6 = 32/3
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Re: In the figure, if QS=6 units and PS=8 units, then what is the length   [#permalink] 10 Oct 2017, 01:35
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