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In triangle ABC above, what is the length of side BC? 1)

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Senior Manager
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In triangle ABC above, what is the length of side BC? 1) [#permalink] New post 14 Nov 2006, 11:10
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In triangle ABC above, what is the length of side BC?

1) Line segment AD has lenght 6.

2) x= 36
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Senior Manager
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 [#permalink] New post 14 Nov 2006, 13:23
Why A????

What is your reasoning???
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 [#permalink] New post 14 Nov 2006, 14:55
From1
DAC + ABD = 2X
=> X + ABD = 2X
=> ABD = X
So AD = DB again DB = BC
BC = 6

But from hint 2 ..we don’t know the length
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 [#permalink] New post 15 Nov 2006, 18:22
St1:
We know angle DBC = (180 - 4x). We also know angle ABC = (180 - 3x). So angle ABD = 180-3x - 180 + 4x = x.

So ABD is an isoceles triangle and AD = DB = 6. Since DBC is another isoceles triangle and DB = BC, then BC = 6. Sufficient.

St2:
Only tells us DBC is an isoceles triangle but we do not know any of the dimensions.
Insufficient.

Ans A
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 [#permalink] New post 17 Nov 2006, 10:56
You are right.

Oa is A.

Thanks.
  [#permalink] 17 Nov 2006, 10:56
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