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# M04 #12

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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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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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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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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?

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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?

Thanks dzyubam for correcting the question.

AB*BC = itself is product of non-hypotenuse sides.
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02 Oct 2008, 09:10
how do you know AC is the hypotneus?
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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?

Thanks dzyubam for correcting the question.

AB*BC = itself is product of non-hypotenuse sides.
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29 Oct 2008, 21:45
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

In this question, i fail to understand y is D given. Since all points are distinct then how cum BD is the height?
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30 Oct 2008, 07:07
ritula 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

In this question, i fail to understand y is D given. Since all points are distinct then how cum BD is the height?

I think it is B. from the information given, AC has to be hypoteneous. Then AB and AC become non-hypoteneous sides. so st taement 2 is suff.

Source?
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30 Oct 2008, 07:11
Yes, I have had this qs in one of the tests , the QA was B i remember. Can you pls check if its D ? because i think its clearly B.
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30 Oct 2008, 22:50
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.
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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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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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05 Dec 2008, 13:28
This was a poorly written question. It could easily be argued that AB and BC are not "non-hypotenuse sides" because they are the hypotenuses of triangles ABD and BDC, respectively. BD is the only side in the entire problem that is not the hypotenuse of any triangle. Overall, very confusing. Could be improved with either an accompanying picture or with clarifying language in the problem. It was an easy problem - understanding the information they were giving you was ambiguous at best.
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05 Dec 2008, 21:14
JorgeStevenson wrote:
This was a poorly written question. It could easily be argued that AB and BC are not "non-hypotenuse sides" because they are the hypotenuses of triangles ABD and BDC, respectively. BD is the only side in the entire problem that is not the hypotenuse of any triangle. Overall, very confusing. Could be improved with either an accompanying picture or with clarifying language in the problem. It was an easy problem - understanding the information they were giving you was ambiguous at best.

To me question stems is looking very clear:

we know that triangle ABC is a right triangle, we know that the 4 points are distinct. That means that BD is the Height to the hypotenuse AC, you don't even need to draw a triangle to figure that.
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24 Jan 2009, 21:38
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

I got so confused with why D is listed and if the order can be A,B, C or could be different. Is this intentional?
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25 Jan 2009, 01:31
ConkergMat 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

I got so confused with why D is listed and if the order can be A,B, C or could be different. Is this intentional?

Is it B?
Here is how I understand it: A triangle has 3 heights. In right triangle, the two of them are the sides of the triangle and a third one is on the right angle to the hypotenuse. In this question, it is this third one. If it wouldn't be the case, the question would use two of the letters from "ABC".
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21 Aug 2009, 19:51
"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?"

The language of this question appears at odds with the author's intent.

With respect to a triangle, the word "height" really only means "a line segment perpendicular to a triangle's edge, of a length equal to the distance of that edge from the opposite vertex." Height BD may or may not land D on the perimeter of the triangle. A line segment labeled "height" may just as easily be outside the triangle as inside the triangle, and is indeed outside the triangle in one example from a Grade 6 math text. "Height" means whatever helps you calculate the area of a triangle most easily; GMAC's OG12 does not use this term.

The term "altitude" would make the answer explanation work. From OG12 p.130: "The altitude of a triangle is the segment drawn from a vertex perpendicular to the side opposite that vertex." D must then lie on the perimeter of right triangle ABC, and B must be opposite the hypotenuse AC for D to be distinct from A and C.

Since GMAC does apparently regard "altitude" as fair game on the exam, and even gives the area of a triangle as "0.5*(base plus altitude)" on OG12 p.130, is there any chance of having this question amended to refer to "altitude BD" rather than "height BD" for future M04 takers?
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21 Aug 2009, 20:04
Just stick to "Distinct points A , B , C , D" form a right triangle ABC with a height BD.

That mean AC is the hypotenuse side.

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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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ezte....guau!   [#permalink] 10 Oct 2009, 14:37

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# M04 #12

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