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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 ?

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.

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.

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?

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.
_________________

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?
_________________

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 \(z=\sqrt{40}\)...

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

Show Tags

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.

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).
_________________

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 3373 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.

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

Show Tags

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 ? . _________________

Click +1 Kudos if my post helped

gmatclubot

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

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