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The length of segmant PS

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The length of segmant PS [#permalink]  19 Mar 2018, 10:42
Expert's post
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Question Stats:

50% (00:46) correct 50% (02:07) wrong based on 10 sessions
Attachment:

PQR.jpg [ 10.29 KiB | Viewed 409 times ]

The area of $$\Delta PQS$$ is 45.

 Quantity A Quantity B The length of segment PS The length of segment SR

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Last edited by Carcass on 20 Mar 2018, 02:47, edited 1 time in total.
Edited the stem
Manager
Joined: 22 Feb 2018
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Kudos [?]: 77 [1] , given: 15

Re: The length of segmant PS [#permalink]  19 Mar 2018, 15:56
1
KUDOS
As PRQ is right side we have:
PR^2 + PQ^2 = RQ^2
(PS +SR)^2 + 12^2 = 20^2
(PS +SR) = 16
We know That in a triangle, the summation of each two sides is more than the third one, so:
12 < PS + QS
20 < SR + QS so 20- 8 < (SR-8) + QS
From above two equations, we recognize that SR is at least 8 more than PS. So SR is more than PS.
NOT SURE IT'S CORRECT OR NOT

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Re: The length of segmant PS [#permalink]  19 Mar 2018, 17:28
1
KUDOS
As PRQ is right side we have:
PR^2 + PQ^2 = RQ^2
(PS +SR)^2 + 12^2 = 20^2
(PS +SR) = 16
We know That in a triangle, the summation of each two sides is more than the third one, so:
12 < PS + QS
20 < SR + QS so 20- 8 < (SR-8) + QS
From above two equations, we recognize that SR is at least 8 more than PS. So SR is more than PS.
NOT SURE IT'S CORRECT OR NOT

how can you make sure "20- 8 < (SR-8) + QS" ?

I think the ans is D.

if we cut PR into half >>> PS=SR=8

then QS would be around 14. which is applicable for a right trianle with sides 12-8-14.XX
Manager
Joined: 27 Sep 2017
Posts: 112
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Kudos [?]: 29 [1] , given: 4

Re: The length of segmant PS [#permalink]  19 Mar 2018, 17:29
1
KUDOS
Carcass wrote:
Attachment:
PQR.jpg

 Quantity A Quantity B The length of segment PS The length of segment SR

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

Please correct the ans . ANS should be D
Intern
Joined: 19 Mar 2018
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Kudos [?]: 8 [1] , given: 11

Re: The length of segmant PS [#permalink]  20 Mar 2018, 00:12
1
KUDOS
Is It D? we need more information to conclude (Data Insufficient )
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Posts: 5199
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Kudos [?]: 1048 [0], given: 4690

Re: The length of segmant PS [#permalink]  20 Mar 2018, 02:46
Expert's post
Sorry guys, the question is missing of the stem. My fault. Could happen when the workload is at the top

really sorry. Fixed the stem in the question above. Kudos.

Thank you so much.

PS: for this reason I love this community
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Kudos [?]: 8 [1] , given: 10

Re: The length of segmant PS [#permalink]  07 Apr 2018, 09:50
1
KUDOS
45 = 1/2b (12) so PS is 7.5
12^2 + b^2 = 20^2 b or PR is 16
RS = PR - PS (16-7.5)= 8.5 is RS
Re: The length of segmant PS   [#permalink] 07 Apr 2018, 09:50
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