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M04-12

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Re: M04-12  [#permalink]

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New post 14 Sep 2016, 04:58
Hi Bunuel,
I still feel B doesn't necessarily need to be the right angle
I considered this scenario

A D
|
|
C-------B

ACB is right angled at C and D doesn't coincide with A and BD is height of the triangle ABC. AB is hypotenus.
Please explain thanks!
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New post 14 Sep 2016, 05:01
D is right above B somehow posting is trimming the space between A and D
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New post 28 Sep 2016, 05:58
I totally missed the part about A, B, C, and D each being a distinct point on a plane. I was like, "how do we know that angle B is 90 degrees?" then when I finally saw the word "distinct," everything clicked. :lol:
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New post 09 Feb 2017, 00:34
Sachin07 wrote:
Cant dis problem b solved by 30-60-90 theorem (as we know the point A B C D are distinct points, so AB is not equal to BC) thus making stmnt 1 sufficient to find the value of BC and hence the value of AB*BC.


Why should the triangle be 30-60-90 one? Not all right triangle have 30-60-90 angles.
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Re M04-12  [#permalink]

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New post 21 May 2017, 18:33
I think this the explanation isn't clear enough, please elaborate. When the 2nd statement says "The product of the non-hypotenuse sides of triangle ABC is equal to 24", can it not mean that the product of BD*AC =24 or BD*CB = 24. As BD is part of the triangle ABC. I think I overthought this question!
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New post 21 May 2017, 19:03
vil1 wrote:
I think this the explanation isn't clear enough, please elaborate. When the 2nd statement says "The product of the non-hypotenuse sides of triangle ABC is equal to 24", can it not mean that the product of BD*AC =24 or BD*CB = 24. As BD is part of the triangle ABC. I think I overthought this question!


Non-hypotenuse sides of triangle ABC are AB and BC.
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Re: M04-12  [#permalink]

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New post 04 Dec 2017, 21:32
In the second statement, it says the product of 2 non hypotenuse sides is 24. Then in that case, it can have multiple answers such as 2*12, 3*8, 4*6. With help of statement 1, we can say that AB*AC is 6*4 only. Hence, my doubt is, why cant the answer be C ?
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New post 04 Dec 2017, 21:48
chetanb12 wrote:
In the second statement, it says the product of 2 non hypotenuse sides is 24. Then in that case, it can have multiple answers such as 2*12, 3*8, 4*6. With help of statement 1, we can say that AB*AC is 6*4 only. Hence, my doubt is, why cant the answer be C ?


The question asks to find the value of AB*BC. (2) says that AB*BC = 24. We have our answer! Does it matter whether it's 1*24, 1/2*48, 500*24/500, or anything else?
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Re: M04-12  [#permalink]

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New post 01 Jan 2018, 05:28
Hi Bunuel.

Statement 2 says that the product of non hypotenuse sides is 24. Why are we not considering BD here?

Can among AB, BC or BD, any of the two sides be non hypotenuse side ?

Happy new Year.

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New post 01 Jan 2018, 05:31
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sandysilva wrote:
Hi Bunuel.

Statement 2 says that the product of non hypotenuse sides is 24. Why are we not considering BD here?

Can among AB, BC or BD, any of the two sides be non hypotenuse side ?

Happy new Year.

Regards


(2) says: The product of the non-hypotenuse sides of triangle ABC is equal to 24. In triangle ABC, AC is hypotenuse, so non-hypotenuse sides are AB and BC. I think this is shown/explained on previous two pages several times.
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Re: M04-12  [#permalink]

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New post 01 Jan 2018, 05:35
Bunuel wrote:
sandysilva wrote:
Hi Bunuel.

Statement 2 says that the product of non hypotenuse sides is 24. Why are we not considering BD here?

Can among AB, BC or BD, any of the two sides be non hypotenuse side ?

Happy new Year.

Regards


(2) says: The product of the non-hypotenuse sides of triangle ABC is equal to 24. In triangle ABC, AC is hypotenuse, so non-hypotenuse sides are AB and BC. I think this is shown/explained on previous two pages several times.


Thank you for your prompt reply. Sorry! I might have missed to check thoroughly.
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Re M04-12  [#permalink]

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New post 09 Jan 2018, 19:21
I think this is a high-quality question and the explanation isn't clear enough, please elaborate. Hi,
in this right angled triangle we can take AB or BC as the height ? why are we taking another height BD? im also not clear how we know that B must be the right angle if BD is the height?kindly explain im really confused.
Thanks a lot in advance.
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New post 09 Jan 2018, 19:53
Furqan90 wrote:
I think this is a high-quality question and the explanation isn't clear enough, please elaborate. Hi,
in this right angled triangle we can take AB or BC as the height ? why are we taking another height BD? im also not clear how we know that B must be the right angle if BD is the height?kindly explain im really confused.
Thanks a lot in advance.


I think all your doubts are already answered in this topic. Please read the whole discussion.

Hope it helps.
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Re: M04-12  [#permalink]

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New post 22 Jan 2018, 18:27
wow.. "distinct points" made all the difference and drawing the triangle is the trick, excellent question and OA!!
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New post 26 Jan 2018, 00:55
I don't understand why 2) alone is sufficient? AB*AC=24 --> could be 3*8 or 8*3 or 4*6 or 6*4?

Please explain me, when I am wrong.
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New post 26 Jan 2018, 00:58
MaxKirchmayer wrote:
I don't understand why 2) alone is sufficient? AB*AC=24 --> could be 3*8 or 8*3 or 4*6 or 6*4?

Please explain me, when I am wrong.


The question asks: what is the value of AB*BC? We got that it's 24. I does not matter what individual values of AB and BC are.
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Re: M04-12  [#permalink]

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New post 28 Oct 2018, 22:35
Bunuel wrote:
ishitathukral wrote:
first option says AB =6
doesnt it imply that the sides are 6,8,10?


No.

Knowing that one side of a right triangle is 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 \(z=\sqrt{40}\)...

Thanks Bunnel for the nice explanation

Bunnel/Chetan

I have a query,

If vertices are said to be integers then ,will that follow the pythogorean triplet like 6,8,10 and answer change.



Thanks
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Re: M04-12 &nbs [#permalink] 28 Oct 2018, 22:35

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