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

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Math Expert
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In the figure above, what is the length of PQ times the length of RS?  [#permalink]

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20 Nov 2015, 00:53
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Question Stats:

50% (01:22) correct 50% (02:00) wrong based on 137 sessions

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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.

Attachment:

PR-B3-07.JPG [ 3.79 KiB | Viewed 2289 times ]

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Re: In the figure above, what is the length of PQ times the length of RS?  [#permalink]

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20 Nov 2015, 01:12
2
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

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Re: In the figure above, what is the length of PQ times the length of RS?  [#permalink]

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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.

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

Verbal Forum Moderator
Status: Greatness begins beyond your comfort zone
Joined: 08 Dec 2013
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Concentration: General Management, Strategy
Schools: Kelley '20, ISB '19
GPA: 3.2
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Re: In the figure above, what is the length of PQ times the length of RS?  [#permalink]

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20 Nov 2015, 11:45
1
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.

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

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 !!
_________________

When everything seems to be going against you, remember that the airplane takes off against the wind, not with it. - Henry Ford
The Moment You Think About Giving Up, Think Of The Reason Why You Held On So Long
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Posts: 34
Re: In the figure above, what is the length of PQ times the length of RS?  [#permalink]

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21 Nov 2015, 12:46
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.

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

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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Joined: 27 May 2015
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Re: In the figure above, what is the length of PQ times the length of RS?  [#permalink]

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29 Jan 2018, 19:52
Cant we use RS=PQ/2 ?
Math Expert
Joined: 02 Sep 2009
Posts: 48037
Re: In the figure above, what is the length of PQ times the length of RS?  [#permalink]

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29 Jan 2018, 20:55
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.

For other subjects:
ALL YOU NEED FOR QUANT ! ! !

Hope it helps.
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Re: In the figure above, what is the length of PQ times the length of RS?  [#permalink]

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01 Feb 2018, 01:13
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.

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? &nbs [#permalink] 01 Feb 2018, 01:13
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