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M04 #12

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M04 #12 [#permalink] New post 10 Aug 2008, 11:56
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Distinct points A, B, C, 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

REVISED VERSION OF THIS QUESTION WITH A SOLUTION: m04-68703-80.html#p1108189
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Re: M04 #12 [#permalink] New post 20 Jul 2010, 05:05
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hope this will help
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Re: M04 #12 [#permalink] New post 27 Jul 2012, 07:25
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BELOW IS REVISED VERSION OF THIS QUESTION WITH A SOLUTION:

A, B, C, and D are distinct points on a plane. If triangle ABC is a 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.

Answer: B.

Hope it's clear.
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Re: ezte....guau! [#permalink] New post 10 Oct 2010, 05:07
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ans will be B only..as we have to find ab*bc..which is given in 2 stmt..
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Re: m04, Q 12 [#permalink] New post 31 Oct 2008, 08:35
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ritula wrote:
Guys , I think I cldnt explain my problem. Im not talking of OA. OA is B indeed 2 which i agree. My question is why is point D given in the question. there is no need for this. In case its a triangle, there have 2b only 3 points na? also BD height is confusing me.


D is given to make question tough and intresting. Also it gave a twist in the question.
The way this question is designed, D is required and correctly signals the right angle as well.
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Re: m04, Q 12 [#permalink] New post 05 Dec 2008, 10:02
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ritula wrote:
Guys , I think I cldnt explain my problem. Im not talking of OA. OA is B indeed 2 which i agree. My question is why is point D given in the question. there is no need for this. In case its a triangle, there have 2b only 3 points na? also BD height is confusing me.


D is given to make question tough and intresting. Also it gave a twist in the question.
The way this question is designed, D is required and correctly signals the right angle as well.


BD is the Height to the Hypotenuse.
In the right trinagle the non hypotenuse sides are the other heigts of the triangle. It is given in order to identify the Hypotenuse.
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ezte....guau! [#permalink] New post 10 Oct 2009, 14:37
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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
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Re: ezte....guau! [#permalink] New post 10 Oct 2009, 16:14
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Since the triangle has ABC as a right triangle, the square of the triangle would be multiple of two non hypothenuse sides of the triangle divided by two.
Statement ! just provides us with the information about the measurement of side AB
Not sufficient.

Hence, we know that 2) The product of the non-hypotenuse sides is equal to 24, which is multiple of sides AB and BC (reuqired sides)
We can conclude that Statement 2 is sufficient to answer the question.

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Re: ezte....guau! [#permalink] New post 08 Nov 2009, 15:31
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The point D is a misleading trap here. You don't need that information.

Rt Triangle ABC - What's AB *BC - or one leg * hypotenuse

Statement 1 - not enough clearly

Statement 2 - product of two legs given,
using the theorm hypotenuse^2 = leg1^2 + leg2^2
leg1 *leg2 = 24.

Asked to find leg1*hypotenuse. From the above two equations it can easily be determined. Hence B is sufficient.
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Re: M04 #12 [#permalink] New post 20 Jul 2010, 04:07
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This is a tricky one
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Re: M04 #12 [#permalink] New post 20 Jul 2010, 04:11
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Since all points are distinct and BD is the height...D lies on AC and AC is hypotenueus.
The right angle is formed at B.
In all other scenarios, D equals either A/C

Answer: B
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Re: M04 #12 [#permalink] New post 20 Jul 2010, 06:10
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The triangle looks like this:

Image

BD being the height establishes that B must be across from the hypotenuse. This means AB and BA are the legs of the triangle.
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Re: M04 #12 [#permalink] New post 31 Aug 2011, 05:40
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ABC is a right triangle......the right angle can be any one out of A, B or C? Why does it have to be only B?
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Re: M04 #12 [#permalink] New post 05 Sep 2011, 13:49
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I just took this test.
I had answered E.

I assumed that D should be a distinct pt. However, if the triangle is right-angled at A then the altitude BD can be drawn outside the triangular region ABC such that the BD will be parallel to AB or AC. In this case, the value of AB*BC will be 6*sqrt(52), which is different from the ans that we get if we assume that the triangle is right angled at B.

Please let me know if it I'm missing something.
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Re: M04-Q12 [#permalink] New post 11 Aug 2008, 21:34
Unless one of your points is on one of the straight lines, you have a quadrilateral and not a triangle.
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Re: M04-Q12 [#permalink] New post 14 Aug 2008, 12:12
Tvisha wrote:
Distinct points A , B , C , D form a right triangle with a height . What is the value of AB times BC?

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

could any one explain this?



Can you check the question.. looks like something missing.
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Re: M04-Q12 [#permalink] New post 21 Aug 2008, 00:44
Tvisha wrote:
Distinct points A , B , C , 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

could any one explain this?

I've added the missing text.
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Re: M04-Q12 [#permalink] New post 21 Aug 2008, 06:20
dzyubam wrote:
Tvisha wrote:
Distinct points A , B , C , 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

could any one explain this?

I've added the missing text.


Thanks dzyubam for correcting the question.

Answer should be B.
AB*BC = itself is product of non-hypotenuse sides.
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Re: M04-Q12 [#permalink] New post 02 Oct 2008, 09:10
how do you know AC is the hypotneus?
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Re: M04-Q12 [#permalink] New post 02 Oct 2008, 12:03
hi,

I have a small question, If ABC froms a right angled triangle then the height should be either AB or BC or AC, then how did D come into the picture. I think this can be possible only when the point D coincides with any one of A, B or C.

Could you explain if i got this wrong.

Thanks

x2suresh wrote:
dzyubam wrote:
Tvisha wrote:
Distinct points A , B , C , 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

could any one explain this?

I've added the missing text.


Thanks dzyubam for correcting the question.

Answer should be B.
AB*BC = itself is product of non-hypotenuse sides.
Re: M04-Q12   [#permalink] 02 Oct 2008, 12:03
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