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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:

54% (01:55) correct 45% (01:12) wrong based on 48 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: 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 2238 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] 12 Mar 2014, 09:02
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