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

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A, B, C, and D are distinct points on a plane. If triangle A [#permalink]

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19 Mar 2012, 10:23
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55% (00:58) correct 45% (01:22) wrong based on 488 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.

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A, B, C, and D are distinct points on a plane. If triangle A [#permalink]

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19 Mar 2012, 10:50
1
2
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.

Hope it's clear.
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Re: A, B, C, and D are distinct points on a plane. If triangle A [#permalink]

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31 May 2012, 16:54
Could someone please draw the figure for this? thanks
Math Expert
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Posts: 46128
Re: A, B, C, and D are distinct points on a plane. If triangle A [#permalink]

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01 Jun 2012, 02:31
1
karthiksms wrote:
Could someone please draw the figure for this? thanks

Here you go:
Attachment:

ABC.png [ 5.22 KiB | Viewed 26079 times ]

Hope it helps.
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Re: A, B, C, and D are distinct points on a plane. If triangle A [#permalink]

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02 Sep 2012, 15:40
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: A, B, C, and D are distinct points on a plane. If triangle A [#permalink]

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20 Sep 2012, 21:46
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: A, B, C, and D are distinct points on a plane. If triangle A [#permalink]

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21 Sep 2012, 01:42
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: A, B, C, and D are distinct points on a plane. If triangle A [#permalink]

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12 Mar 2014, 09:52
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: A, B, C, and D are distinct points on a plane. If triangle A [#permalink]

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12 Mar 2014, 09:57
1
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: A, B, C, and D are distinct points on a plane. If triangle A [#permalink]

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12 Mar 2014, 10:02
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: A, B, C, and D are distinct points on a plane. If triangle A [#permalink]

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29 Mar 2014, 14:42
For statement 2:

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

Thanks
Cheers
J
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Posts: 46128
Re: A, B, C, and D are distinct points on a plane. If triangle A [#permalink]

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29 Mar 2014, 14:49
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: A, B, C, and D are distinct points on a plane. If triangle A [#permalink]

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30 Mar 2014, 13:09
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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Posts: 46128
Re: A, B, C, and D are distinct points on a plane. If triangle A [#permalink]

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31 Mar 2014, 02:10
1
1
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: A, B, C, and D are distinct points on a plane. If triangle A [#permalink]

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31 Mar 2014, 14:15
Awesome Bunuel,Thanks a lot.
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Posts: 213
Re: A, B, C, and D are distinct points on a plane. If triangle A [#permalink]

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17 Apr 2014, 11:16
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.
Intern
Joined: 19 Jan 2008
Posts: 17
Re: A, B, C, and D are distinct points on a plane. If triangle A [#permalink]

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17 Apr 2014, 11:31
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.
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Posts: 46128
Re: A, B, C, and D are distinct points on a plane. If triangle A [#permalink]

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18 Apr 2014, 02:42
1
PathFinder007 wrote:
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.

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).
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Re: A, B, C, and D are distinct points on a plane. If triangle A [#permalink]

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10 May 2014, 05:02
enigma123 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.

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

Attachment:

TRIANGLE 1.jpg [ 112.83 KiB | Viewed 7433 times ]

If the triangle is as shown in the attachment above then in statement 2 when it says the product of the non hypotenuse sides is 24
then we could also take in ∆ ABD hypotenuse is AB and non hypotenuse sides as AD *BD

also in ∆ BDC hypotenuse is BC and non hypotenuse sides are BD*DC

So statement 2 seems a bit ambiguous.

There are actually 3 right triangles in points ABCD , ∆ ABC, ∆ ABD, ∆ BDC so when they say product of non hypotenuse side
is 24 , we could choose any right triangle among these 3 and take 2 of its non hypotenuse sides .

Why are we assuming that the question is talking of ∆ ABC when it says product of non hypotenuse sides
is 24.

If question had said product of non hypotenuse sides of largest triangle or product of non hypotenuse sides of triangle ABC then 2 could surely be enough.

Please correct me if I am wrong.
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A, B, C, and D are distinct points on a plane. If triangle A [#permalink]

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01 Feb 2015, 10:08
qlx wrote:
enigma123 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.

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

Attachment:
TRIANGLE 1.jpg

If the triangle is as shown in the attachment above then in statement 2 when it says the product of the non hypotenuse sides is 24
then we could also take in ∆ ABD hypotenuse is AB and non hypotenuse sides as AD *BD

also in ∆ BDC hypotenuse is BC and non hypotenuse sides are BD*DC

So statement 2 seems a bit ambiguous.

There are actually 3 right triangles in points ABCD , ∆ ABC, ∆ ABD, ∆ BDC so when they say product of non hypotenuse side
is 24 , we could choose any right triangle among these 3 and take 2 of its non hypotenuse sides .

Why are we assuming that the question is talking of ∆ ABC when it says product of non hypotenuse sides
is 24.

If question had said product of non hypotenuse sides of largest triangle or product of non hypotenuse sides of triangle ABC then 2 could surely be enough
.

Please correct me if I am wrong.

Dear Bunuel,I agree with glx and I asked myself the same question above. Why we

assuming that the question is talking about ∆ ABC while the statement 2 did not say that the product of non

hypotenuse sides of largest triangle is 24 ? .

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A, B, C, and D are distinct points on a plane. If triangle A   [#permalink] 01 Feb 2015, 10:08

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