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# If distinct points A, B, C, and D form a right triangle ABC

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If distinct points A, B, C, and D form a right triangle ABC [#permalink]  19 Mar 2012, 09:23
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Question Stats:

48% (02:02) correct 51% (01:34) wrong based on 111 sessions
If distinct points A, B, C, and D form a right triangle ABC with a height BD, what is the value of AB times BC ?

(1) AB = 6.
(2) The product of the non-hypotenuse sides is equal to 24.

I am struggling to understand the solution given in GMATCLub Test. Can you please explain how statement 2 is sufficient to answer this question?
[Reveal] Spoiler: OA

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Re: If distinct points A, B, C, and D form a right triangle ABC [#permalink]  31 Mar 2014, 01:10
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Expert's post
ankushbassi wrote:
If the perpendicular is given as 6,that means its a right triangle with base=8 and hypotenuse =10.
Is my understanding wrong?

Do you mean that since BD=6, then DC must be 8 and BC must be 10? That's not true.

This is a common trap.

Knowing that one of the legs is to 6 DOES NOT mean that the sides of the right triangle necessarily must be in the ratio of Pythagorean triple - 6:8:10. Or in other words: if 6^2+y^2=z^2 DOES NOT mean that y=8 and z=10. Certainly this is one of the possibilities but definitely not the only one. In fact 6^2+y^2=z^2 has infinitely many solutions for y and z and only one of them is y=8 and z=10.

For example: y=1 and z=\sqrt{37} or y=2 and z=\sqrt{40}...

I collected the questions which use this trap:
the-circular-base-of-an-above-ground-swimming-pool-lies-in-a-167645.html
figure-abcd-is-a-rectangle-with-sides-of-length-x-centimete-48899.html
in-right-triangle-abc-bc-is-the-hypotenuse-if-bc-is-13-and-163591.html
m22-73309-20.html
if-vertices-of-a-triangle-have-coordinates-2-2-3-2-and-82159-20.html
if-p-is-the-perimeter-of-rectangle-q-what-is-the-value-of-p-135832.html
if-the-diagonal-of-rectangle-z-is-d-and-the-perimeter-of-104205.html
what-is-the-area-of-rectangular-region-r-105414.html
what-is-the-perimeter-of-rectangle-r-96381.html
pythagorean-triples-131161.html
given-that-abcd-is-a-rectangle-is-the-area-of-triangle-abe-127051.html
m13-q5-69732-20.html#p1176059
m20-07-triangle-inside-a-circle-71559.html
what-is-the-perimeter-of-rectangle-r-96381.html
what-is-the-area-of-rectangular-region-r-166186.html

Hope this helps.
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Re: Triangle ABC [#permalink]  19 Mar 2012, 09:50
Expert's post
If distinct points A, B, C, and D form a right triangle ABC with a height BD, what is the value of AB times BC ?

BD is a height means that B is a right angle and AC is a hypotenuse (so BD is a height from right angle B to the hypotenuse AC). Question thus asks about the product of non-hypotenuse sides AB and BC.

(1) AB = 6. Clearly insufficient.
(2) The product of the non-hypotenuse sides is equal to 24 --> directly gives us the value of AB*BC. Sufficient.

Hope it's clear.
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Re: If distinct points A, B, C, and D form a right triangle ABC [#permalink]  31 May 2012, 15:54
Could someone please draw the figure for this? thanks
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Re: If distinct points A, B, C, and D form a right triangle ABC [#permalink]  01 Jun 2012, 01:31
Expert's post
karthiksms wrote:
Could someone please draw the figure for this? thanks

Here you go:
Attachment:

ABC.png [ 5.22 KiB | Viewed 2811 times ]

Hope it helps.
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Re: If distinct points A, B, C, and D form a right triangle ABC [#permalink]  02 Sep 2012, 14:40
Key to this question is "Distinct point" and "Right Triangle". Height BD cannot be AB otherwise the points A=D. So the height BD has to come out of point B (The 90* angle) and intersect AC.
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Re: If distinct points A, B, C, and D form a right triangle ABC [#permalink]  20 Sep 2012, 20:46
Bunuel wrote:
karthiksms wrote:
Could someone please draw the figure for this? thanks

Here you go:
Attachment:
ABC.png

Hope it helps.

Bunuel, but D doesn't necessarily have to be inside of the triangle right? So what if point D was outside of the triangle vertically above C in your diagram, and equivalent to the original line specified BD, except outside of the triangle? If we kept the same triangle from your diagram, and instead changed the problem to say CD is a height of the triangle with D being vertically about C, then B would still be the right angle and the statements would be inefficient. Am I making a mistake in thinking this?
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Re: If distinct points A, B, C, and D form a right triangle ABC [#permalink]  21 Sep 2012, 00:42
Expert's post
dandarth1 wrote:
Bunuel wrote:
karthiksms wrote:
Could someone please draw the figure for this? thanks

Here you go:
Attachment:
ABC.png

Hope it helps.

Bunuel, but D doesn't necessarily have to be inside of the triangle right? So what if point D was outside of the triangle vertically above C in your diagram, and equivalent to the original line specified BD, except outside of the triangle? If we kept the same triangle from your diagram, and instead changed the problem to say CD is a height of the triangle with D being vertically about C, then B would still be the right angle and the statements would be inefficient. Am I making a mistake in thinking this?

We are told that "points A, B, C, and D form a right triangle ABC", so D must be on one of the sides.
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Re: If distinct points A, B, C, and D form a right triangle ABC [#permalink]  12 Mar 2014, 08:52
my question is.. we are asked ab times bc?

bt in statement 2. we have given ab*bc=24? how can we get separate value of both from this?
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Re: If distinct points A, B, C, and D form a right triangle ABC [#permalink]  12 Mar 2014, 08:57
Expert's post
sanjoo wrote:
my question is.. we are asked ab times bc?

bt in statement 2. we have given ab*bc=24? how can we get separate value of both from this?

We are asked to find AB*BC. (2) says that AB*BC=24. So, we have the value which we wanted to find. Why do we need the values of AB and BC?
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Re: If distinct points A, B, C, and D form a right triangle ABC [#permalink]  12 Mar 2014, 09:02
Bunuel wrote:
sanjoo wrote:
my question is.. we are asked ab times bc?

bt in statement 2. we have given ab*bc=24? how can we get separate value of both from this?

We are asked to find AB*BC. (2) says that AB*BC=24. So, we have the value which we wanted to find. Why do we need the values of AB and BC?

Oh doesnt ab times bc mean ab/bc? or bc/ab? Shit! that means i didnt get the question clearly..!!

if ab times bc=ab*bc..fine..then i got the solution !
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Re: If distinct points A, B, C, and D form a right triangle ABC [#permalink]  29 Mar 2014, 13:42
For statement 2:

Why can't the product BD*DC = 24 instead of being AB*BC?

Thanks
Cheers
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Re: If distinct points A, B, C, and D form a right triangle ABC [#permalink]  29 Mar 2014, 13:49
Expert's post
jlgdr wrote:
For statement 2:

Why can't the product BD*DC = 24 instead of being AB*BC?

Thanks
Cheers
J

BD is a height means that B is a right angle and AC is a hypotenuse (so BD is a height from right angle B to the hypotenuse AC).

(2) says that the product of the non-hypotenuse sides is equal to 24, the non-hypotenuse sides are AB and BC.

Hope it's clear.
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Re: If distinct points A, B, C, and D form a right triangle ABC [#permalink]  30 Mar 2014, 12:09
If the perpendicular is given as 6,that means its a right triangle with base=8 and hypotenuse =10.
Is my understanding wrong?
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Re: If distinct points A, B, C, and D form a right triangle ABC [#permalink]  31 Mar 2014, 13:15
Awesome Bunuel,Thanks a lot.
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Re: If distinct points A, B, C, and D form a right triangle ABC [#permalink]  17 Apr 2014, 10:16
Bunuel wrote:
karthiksms wrote:
Could someone please draw the figure for this? thanks

Here you go:
Attachment:
ABC.png

Hope it helps.

Hi Bunnel,

I have a small doubt on thic diagram. We know D is 90 degree. But I want to know how B is 90 degree. Is it because we are getting height fron one of the vertices.

Thanks.
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Re: If distinct points A, B, C, and D form a right triangle ABC [#permalink]  17 Apr 2014, 10:31
Since, it is clear that D is the point that has the height.The height of the right triangle always comes form the 90 degree angle,thus B is 90 degree.
Re: If distinct points A, B, C, and D form a right triangle ABC   [#permalink] 17 Apr 2014, 10:31
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