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In triangle ABC angle ABC is 90 degrees. What is the

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In triangle ABC angle ABC is 90 degrees. What is the [#permalink] New post 11 May 2008, 23:27
In triangle ABC angle ABC is 90 degrees. What is the perimeter of the triangle ABC?

1. AB+ BC =7
2. AB/BC =3/4
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Re: M11-triangle [#permalink] New post 11 May 2008, 23:39
C.

Once you know that AB/BC = 3/4 and that AB+BC = 7 you can tell that AB = 3 and BC = 4 and that AC = 5.

But then maybe I'm missing something, cos you wouldn't have posted it if it were this simple :)
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Re: M11-triangle [#permalink] New post 12 May 2008, 06:39
I vote for D!

1. AB+BC=7

AB=0, BC=7
AB=1, BC=6
AB=2, BC=5
AB=3, BC=4

If ABC is a right-angled triangle.. then AC^2=AB^2+BC^2 and this is only possible when AB=3, BC=4 or AB=4, BC=3.. in either case, AC=5!

So perimeter is AB+BC+AC

2. AB/BC=3/4

Then, AC=5 and the perimeter is AB+BC+AC!
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Re: M11-triangle [#permalink] New post 12 May 2008, 06:41
Kalyan - what if AB/BC were 6/8 ?
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Re: M11-triangle [#permalink] New post 12 May 2008, 07:17
i agree with C!

we know the triangle is 90 degree it could be 345 or 51213 triangle i dont know..

1) AB+BC=7..well to get AC..AC^2=AB^2+BC^2... however AB+BC=7 is insuff since AB^2+2ABBC+BC^2=49..i dont know what 2ABBC is equal to..insuff

2) gives the ratio..3/4 ok so i know its a 345 triangle but the sides could easily be 6810..i dont know..

together sufficient..i can solve for BC or AB and I would know AC..
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Re: M11-triangle [#permalink] New post 12 May 2008, 07:21
Kalyan wrote:
I vote for D!

1. AB+BC=7

AB=0, BC=7
AB=1, BC=6
AB=2, BC=5
AB=3, BC=4

If ABC is a right-angled triangle.. then AC^2=AB^2+BC^2 and this is only possible when AB=3, BC=4 or AB=4, BC=3.. in either case, AC=5!

So perimeter is AB+BC+AC

2. AB/BC=3/4

Then, AC=5 and the perimeter is AB+BC+AC!


I think D is incorrect. C has to be correct.

In the case of #1, why can't AB = 3.5 and BC = 3.5, which in that case would not yield AC = 5.

It does state that AB and BC are integers. Therefore, I think you need both #1 and #2 to answer this question.
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Re: M11-triangle [#permalink] New post 12 May 2008, 07:31
sondenso wrote:
In triangle ABC angle ABC is 90 degrees. What is the perimeter of the triangle ABC?

1. AB+ BC =7
2. AB/BC =3/4


1. this could have two answers, either, 3 + 4 = 7 or you could play with 3.5 on each side as well? so def. insuff.

2. ab/bc = 3/4 = countless no. combinations. but since 90 degrees@angle abc. this must that ac = 5. but we just don't know if its 6, 8, 10 or 3, 4, 5 therefore insuff.

3. combining them would mean that its 1. 90 degrees at angle abc 2. sides in ratios of 3,4,5. and if 3. if ab +bc =7. then C is suff.

but yeah, a bit too good to be true here?
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Re: M11-triangle [#permalink] New post 12 May 2008, 07:41
I think A could be right as well.
By AB+BC=7 and since this is right angle triange. we have AB and BC= either 3 or 4. Both gives AC=5 means perimeter
AB+BC+AC=12!

I think its good questions, if this comes in the test I might have selected C as well..but careful consideration gives that only A is enough.
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Re: M11-triangle [#permalink] New post 12 May 2008, 07:46
marshpa wrote:
I think A could be right as well.
By AB+BC=7 and since this is right angle triange. we have AB and BC= either 3 or 4. Both gives AC=5 means perimeter
AB+BC+AC=12!

I think its good questions, if this comes in the test I might have selected C as well..but careful consideration gives that only A is enough.



why can't AB = 2, and BC = 5?
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Re: M11-triangle [#permalink] New post 12 May 2008, 20:03
Thanks all of you for the -more- than- I- expected- explaination!

@bsd. Sometime I miss the point, so the easy question will become difficult for me! :lol:

Kalyan wrote:
1. AB+BC=7

AB=0, BC=7
AB=1, BC=6
AB=2, BC=5
AB=3, BC=4

If ABC is a right-angled triangle.. then AC^2=AB^2+BC^2 and this is only possible when AB=3, BC=4 or AB=4, BC=3.. in either case, AC=5!

So perimeter is AB+BC+AC


Thanks Kalyan helping me lengthen my thinking! :lol: you did point out some good possibilities, the same to me, but our reasoning be coutered by this:

rw6183 wrote:
but we just don't know if its 6, 8, 10 or 3, 4, 5 therefore insuff


OA is C :thanks
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Re: M11-triangle   [#permalink] 12 May 2008, 20:03
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