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

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Current Student
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If distinct points A, B, C, and D form a right triangle ABC [#permalink]

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10 Aug 2011, 08:44
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45% (medium)

Question Stats:

65% (01:11) correct 35% (01:39) wrong based on 51 sessions

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A, B, C, and D are distinct points on a plane. If triangle ABC is right angled and BD is a height of this triangle, what is the value of AB times BC ?

(1) AB=6

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

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-b-c-and-d-are-distinct-points-on-a-plane-if-triangle-a-129328.html
[Reveal] Spoiler: OA

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Re: If distinct points A, B, C, and D form a right triangle ABC [#permalink]

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10 Aug 2011, 09:04

Check out the attached diagram.
Attachments

triangle ABC.doc [23.5 KiB]

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Current Student
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Re: If distinct points A, B, C, and D form a right triangle ABC [#permalink]

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10 Aug 2011, 09:08
In that diagram, is AB = BD?

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Re: If distinct points A, B, C, and D form a right triangle ABC [#permalink]

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10 Aug 2011, 09:14
Not necessarily. We cant say that from given info.

The question asks us to calculate AB * BC.

Statement 1, AB = 6. Not sufficient.

Statement 2, AB * BC = 24. This is what we wanted!! Sufficient.

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Re: If distinct points A, B, C, and D form a right triangle ABC [#permalink]

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10 Aug 2011, 09:15
Maybe I'm confused as to what "height of a triangle" is.

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Re: If distinct points A, B, C, and D form a right triangle ABC [#permalink]

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10 Aug 2011, 09:26
The height of the right triangle angle is (always) length of line which is drawn from vertex(point of 90degree) to hypotenuse and which is perpendicular to hypotenuse.

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Re: If distinct points A, B, C, and D form a right triangle ABC [#permalink]

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10 Aug 2011, 09:27
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Rotate the diagram clock-wise. Let the hypotenuse be its base and then find height.

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Re: If distinct points A, B, C, and D form a right triangle ABC [#permalink]

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10 Aug 2011, 12:36
far257 wrote:
In that diagram, is AB = BD?

Note that points A, B, C, and D are distinct....

far257 wrote:
If distinct points A, B, C, and D form a right triangle ABC with a height BD...................

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Re: If distinct points A, B, C, and D form a right triangle ABC [#permalink]

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10 Aug 2011, 12:42
Fistail,

Sorry, I did not get your point.

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Re: If distinct points A, B, C, and D form a right triangle ABC [#permalink]

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10 Aug 2011, 12:55
piyatiwari wrote:
Fistail,

Sorry, I did not get your point.

If points A, B, C, and D are distinct, AB = BD is not possible.

Fistail wrote:
far257 wrote:
In that diagram, is AB = BD?

Note that points A, B, C, and D are distinct....

far257 wrote:
If distinct points A, B, C, and D form a right triangle ABC with a height BD...................

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Re: If distinct points A, B, C, and D form a right triangle ABC [#permalink]

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11 May 2015, 08:36
far257 wrote:
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.

So this question hinges on figuring out which angle is the right angle. According to the OA, ABC must be the right angle, but why? If all points are distinct, drawing a line from point B to point D should be impossible without making D = A or C... right? Unless I'm visualizing this wrong.

halp?

Why can't a non hypotenuse side can be BD. Why we assumed that only non-hypotenuse side are AB & BC.
How do we know that Angle B is 90. why can't it be right angle at angle A and BD is just a altitude from the base BC. OR if it's given that right angle ABC, we always assume that Angle B is 90.

Just thoughts in my mind and want to clear.....

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Re: If distinct points A, B, C, and D form a right triangle ABC [#permalink]

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11 May 2015, 08:39
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Expert's post
A, B, C, and D are distinct points on a plane. If triangle ABC is right angled and BD is a height of this triangle, what is the value of AB times BC ?

Since all points are distinct and BD is a height then B must be a right angle and AC must be 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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-b-c-and-d-are-distinct-points-on-a-plane-if-triangle-a-129328.html
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Re: If distinct points A, B, C, and D form a right triangle ABC   [#permalink] 11 May 2015, 08:39
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