In triangle ABC above, what is the length of side BC?

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In triangle ABC above, what is the length of side BC? [#permalink]

21 Dec 2010, 08:17

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In triangle ABC above, what is the length of side BC?

(1) Line segment AD has length 6
(2) x = 36

[Reveal] Spoiler: OA

Last edited by Bunuel on 23 Jan 2012, 03:05, edited 1 time in total.

Edited the question and added the image

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Re: IN TRIANGLE ABC [#permalink]

21 Dec 2010, 08:31

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In triangle ABC above, what is the length of side BC?

As <BDC=<BCD then the BD=BC. Also as <ADB=180-2x (exterior angle) and the sum of the angles of a triangle is 180 degrees then in triangle ADB we'll have: x+(180-2x)+<ABD=180 --> <ABD=x. Now, we have that <ABD=x=<DAB so AD=BD --> AD=BD=BC.

Question: BC=?

(1) Line segment AD has length 6 --> AD=BD=BC=6. Sufficient.
(2) x = 36 --> we know only angles which is insufficient to get the length of any line segment.

Answer: A.
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Re: IN TRIANGLE ABC [#permalink]

26 Feb 2011, 22:07

the one point that puzzles me is how did you get /BAD = x ?

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Re: IN TRIANGLE ABC [#permalink]

27 Feb 2011, 00:52

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vibhav wrote:

the one point that puzzles me is how did you get /BAD = x ?

It's given that <BAD=x degrees (refer to the diagram in my first post on the page). Some OG books have a typo missing this info (as in vibhav post).
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Re: IN TRIANGLE ABC [#permalink]

27 Feb 2011, 17:56

thanks bunuel! this explains everything!

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Re: Geometry [#permalink]

23 Jan 2012, 00:36

The question asks the length of side BC. From the figure, you can see that triangle BDC is an isosceles triangle with BD = BC. Thus, to know the length of BC, it is okay if we know the length of BD.

Statement 1:
To solve such problems, you have to know that in a triangle, the measure of the exterior angle is equal to the sum of the two non-adjacent angles of the triangle.

That is, in the given figure, for triangle ABD, angle BDC is the exterior angle. Thus, BDC = ABD + BAD
That is, 2x = ABD + x. Thus ABD = x.

Now, you can see that triangle ABD is an isosceles triangle in which AD = BD = 6. Thus, BD = BC = 6. SUFFICIENT

Statement 2:
x = 36 does not tell you anything about the length of any side. INSUFFICIENT

Answer: A
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Re: In triangle ABC above, what is the length of side BC? [#permalink]

25 Jan 2012, 10:45

yeah its A. Bcoz B can only help us to find angle measure but no way we can fund side measrue from there .

so clearly A

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Re: Triangle Problem [#permalink]

20 Mar 2012, 19:09

Using Similar triangles we know that
1) BD = BC (angle BDC = angle BCD)
2) We know angle BDA = 180-2x which means angle ABD = x
3) So, from the second similar triangle we know that angle BAD = angle ABD = x
4) Using similar triangles again; AD = BD
5) Combing 1 and 4; AD = BD = BC.

So, A is sufficient.

We don't really need the angle at all.

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Re: In triangle ABC above, what is the length of side BC? [#permalink]

04 Apr 2012, 07:01

A

we know BD = BC

(A) AD = 6

angle ADB = 180 - 2x

triangle ADB = (180-2x) + x + angle ABD

180 = 180 - 2x + x + angle ABD
x = angle ABD

therefore AD = BD = BC = 6

(B) x = 36
using this information we can only derive that AD = BD = BC , but we dont know value of side

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In triangle ABC above, what is the length of BC ? [#permalink]

20 Apr 2012, 12:16

Attachment:

gmatprep1.jpg [ 46.37 KiB | Viewed 4416 times ]

1) line segment AD has length 6.
2) x=36
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Re: In triangle ABC above, what is the length of BC ? [#permalink]

20 Apr 2012, 12:21

soaringAlone wrote:

Attachment:

gmatprep1.jpg

1) line segment AD has length 6.
2) x=36

Merging similar topics. Please ask if anything remains unclear.
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Re: In triangle ABC above, what is the length of BC ? [#permalink] 20 Apr 2012, 12:21

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In triangle ABC above, what is the length of side BC?

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In triangle ABC above, what is the length of side BC?

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