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# In Triangle ABC, what is the length of side BC? 1) Line

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Director
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In Triangle ABC, what is the length of side BC? 1) Line [#permalink]

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12 Jul 2007, 19:33
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In Triangle ABC, what is the length of side BC?

1) Line segment AD has length 6.

2) x = 36
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TRIANGLE.gif [ 3.52 KiB | Viewed 777 times ]

Manager
Joined: 08 Jul 2007
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12 Jul 2007, 20:01
Sorry for so many edits. We also know that angle BAD is x (this is not in the picture but I remember this problem).

So from the far right triangle, you know that angle CBD=180-2x-2x.

We also know that Angle BDA=180-2x.

So angle ABD=180-(180-2x)-x= 2x-x=x.

Sine ABD=BAD=x, we have an isoceles triangle. So side AD=BD=6 (from statement 1).

Triangle BCD is also isoceles so since BD=6, BC=6. So 1 is sufficient.

2 is not sufficient since we dont have any info about the lengths of the sides.
Director
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12 Jul 2007, 20:14
briks123 wrote:
Sorry for so many edits. We also know that angle BAD is x (this is not in the picture but I remember this problem).

So from the far right triangle, you know that angle CBD=180-2x-2x.

We also know that Angle BDA=180-2x.

So angle ABD=180-(180-2x)-x= 2x-x=x.

Sine ABD=BAD=x, we have an isoceles triangle. So side AD=BD=6 (from statement 1).

Triangle BCD is also isoceles so since BD=6, BC=6. So 1 is sufficient.

2 is not sufficient since we dont have any info about the lengths of the sides.

I'm looking at the problem as I type and I don't see x (or anything) for angle BAD or (DAB).

This is problem number 117 from quantitative review (OG supplement).
Manager
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12 Jul 2007, 20:25
Thats weird. It was on my gmat prep (just looked it up to be sure) and the x was there. Maybe a misprint? seems unlikely! I dont know!
Director
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13 Jul 2007, 06:03
briks123 wrote:
Thats weird. It was on my gmat prep (just looked it up to be sure) and the x was there. Maybe a misprint? seems unlikely! I dont know!

Thanks Briks123! I guess I must have a misprint because I cant get 'A' without x provided.
Director
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13 Jul 2007, 09:10
Yes A is the answer if X is provided in the figure. If not, then its E.
Director
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13 Jul 2007, 19:24
Could we reason that since BDA = 180-2x, ABD and BAD both = x since ABD/BDA/DAB must sum to 180? 180 - (180-2x) = 2x. ABD = 1x and BAD = 1x.
13 Jul 2007, 19:24
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