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In the figure above, what is the length of PQ times the length of RS?

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Bunuel
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In the figure above, what is the length of PQ times the length of RS? [#permalink] New post   20 Nov 2015, 00:53
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In the figure above, what is the length of PQ times the length of RS?

(1) The length of PQ is 5.
(2) The length of QR times the length of PR is equal to 12.

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PR-B3-07.JPG
PR-B3-07.JPG [ 3.79 KiB | Viewed 10808 times ]
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B
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Re: In the figure above, what is the length of PQ times the length of RS? [#permalink] New post   20 Nov 2015, 01:12
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We need to find
PQ*RS =
1. PQ=5
We have no information about RS .
Not sufficient.

2.
QR*PR = 12
Area of triangle PQR = (1/2)* QR * PR
Also , Area of triangle PQR = (1/2)* PQ*RS
=> QR * PR = PQ*RS
Sufficient

Answer B
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Re: In the figure above, what is the length of PQ times the length of RS? [#permalink] New post   20 Nov 2015, 09:31
Bunuel wrote:

In the figure above, what is the length of PQ times the length of RS?

(1) The length of PQ is 5.
(2) The length of QR times the length of PR is equal to 12.

Show Spoiler
Attachment:
PR-B3-07.JPG


From Diagram it is clear that it is a Right Angled Triangle - so
1) PQ = 5, so it will become 3,4,5 Triangle, does not matter which one is 3 or 4, because what I need is Area
Area = 1/2 * 3 * 4 = 6
Now Area Using PQ as Base = 1/2*PQ*RS = 6 = > PQ.RS = 12 (Sufficient)

2) It says QR.PR = 12, which could be 3*4 or 2*6, All we know one of them is acting as the Height. So
QR.PR = 2*Area (Sufficient)

We need PQ.RS = 2 * Area, because RS is Perpendicular to PQ
so PQ*RS = QR*RS

Answer: D
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Re: In the figure above, what is the length of PQ times the length of RS? [#permalink] New post   20 Nov 2015, 11:45
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sandeepmanocha wrote:
Bunuel wrote:

In the figure above, what is the length of PQ times the length of RS?

(1) The length of PQ is 5.
(2) The length of QR times the length of PR is equal to 12.

Show Spoiler
Attachment:
PR-B3-07.JPG


From Diagram it is clear that it is a Right Angled Triangle - so
1) PQ = 5, so it will become 3,4,5 Triangle, does not matter which one is 3 or 4, because what I need is Area
Area = 1/2 * 3 * 4 = 6
Now Area Using PQ as Base = 1/2*PQ*RS = 6 = > PQ.RS = 12 (Sufficient)

2) It says QR.PR = 12, which could be 3*4 or 2*6, All we know one of them is acting as the Height. So
QR.PR = 2*Area (Sufficient)

We need PQ.RS = 2 * Area, because RS is Perpendicular to PQ
so PQ*RS = QR*RS

Answer: D


Hi sandeepmanocha
Just because length of hypotenuse is 5 , the other 2 sides need not be 3 and 4 . The sides need not be a Pythagorean triple .
For example,
If PR and QR are \(\sqrt{(10)}\)and \(\sqrt{(15)}\) , then
10 + 15 = 5^2 = 25
Area = (1/2)*[ \(\sqrt{(10)}\) * \(\sqrt{(15)}\) ]
= (1/2) *\(\sqrt{(150)}\)
= (1/2) * 5 * \(\sqrt{(6)}\)
= 6.12 , which is not equal to 6
So statement 1 will not be sufficient.

Hope it helps !! :)
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Re: In the figure above, what is the length of PQ times the length of RS? [#permalink] New post   21 Nov 2015, 12:46
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Skywalker18 wrote:
sandeepmanocha wrote:
Bunuel wrote:

In the figure above, what is the length of PQ times the length of RS?

(1) The length of PQ is 5.
(2) The length of QR times the length of PR is equal to 12.

Show Spoiler
Attachment:
PR-B3-07.JPG


From Diagram it is clear that it is a Right Angled Triangle - so
1) PQ = 5, so it will become 3,4,5 Triangle, does not matter which one is 3 or 4, because what I need is Area
Area = 1/2 * 3 * 4 = 6
Now Area Using PQ as Base = 1/2*PQ*RS = 6 = > PQ.RS = 12 (Sufficient)

2) It says QR.PR = 12, which could be 3*4 or 2*6, All we know one of them is acting as the Height. So
QR.PR = 2*Area (Sufficient)

We need PQ.RS = 2 * Area, because RS is Perpendicular to PQ
so PQ*RS = QR*RS

Answer: D


Hi sandeepmanocha
Just because length of hypotenuse is 5 , the other 2 sides need not be 3 and 4 . The sides need not be a Pythagorean triple .
For example,
If PR and QR are \(\sqrt{(10)}\)and \(\sqrt{(15)}\) , then
10 + 15 = 5^2 = 25
Area = (1/2)*[ \(\sqrt{(10)}\) * \(\sqrt{(15)}\) ]
= (1/2) *\(\sqrt{(150)}\)
= (1/2) * 5 * \(\sqrt{(6)}\)
= 6.12 , which is not equal to 6
So statement 1 will not be sufficient.

Hope it helps !! :)



It surely does. I think I imagined that they are all Integers :(
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Re: In the figure above, what is the length of PQ times the length of RS? [#permalink] New post   29 Jan 2018, 19:52
Cant we use RS=PQ/2 ?
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Re: In the figure above, what is the length of PQ times the length of RS? [#permalink] New post   29 Jan 2018, 20:55
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mahe wrote:
Cant we use RS=PQ/2 ?


No. In a right triangle the height to the hypotenuse is half the hypotenuse only if the triangle is isosceles.

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Hope it helps.
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Re: In the figure above, what is the length of PQ times the length of RS? [#permalink] New post   01 Feb 2018, 01:13
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Bunuel wrote:

In the figure above, what is the length of PQ times the length of RS?

(1) The length of PQ is 5.
(2) The length of QR times the length of PR is equal to 12.

Show Spoiler
Attachment:
PR-B3-07.JPG


From the figure, Triangle PQR is similar to Triangle RSP. So, we have
\(\frac{QR}{RS} = \frac{PQ}{PR} = \frac{PR}{SP}\)

Statement I:
\(PQ = 5\). We need one more side length to find RS. So, Insufficient.

Statement II:

\(QR * PR = 12\)... From the above Similar Property we have, \(QR * PR = PQ * RS = 12\)

So, sufficient.
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Re: In the figure above, what is the length of PQ times the length of RS? [#permalink] New post   13 Jun 2023, 10:39
Bunuel wrote:

In the figure above, what is the length of PQ times the length of RS?

(1) The length of PQ is 5.
(2) The length of QR times the length of PR is equal to 12.

Show Spoiler
Attachment:
PR-B3-07.JPG



When can we safely say that the given line RS is a median to the hypotenuse?
I thought that RS is a median to the hypotenuse and thus is half of PQ.

Please help.
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Re: In the figure above, what is the length of PQ times the length of RS? [#permalink]
13 Jun 2023, 10:39
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Bunuel
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