Length of a triangle

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cmr209: Senior | Next Rank: 100 Posts; Posts: 42; Joined: Thu Sep 11, 2008 11:07 pm; Location: California; Thanked: 3 times

by cmr209 » Sun Aug 16, 2009 1:36 am

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

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

A 1

B 2

C T

D E

E N

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Source: Beat The GMAT — Problem Solving | Sun Aug 16, 2009 1:36 am

Morgoth: Master | Next Rank: 500 Posts; Posts: 316; Joined: Mon Sep 22, 2008 12:04 amFollowed by: 1 member; Thanked: 36 times

Re: Length of a triangle

by Morgoth » Sun Aug 16, 2009 3:08 am

Question BC=?

AD = BC, let angle ABD = y

x+y = 2x [external triangle theorem]

y = 2x-x = x

y=x

if y=x, then AD=BD.

AD= BD and BC=BD, therefore AD=BC

Statement I

AD=6, therefore BC=6

Sufficient.

Statement II

x=36, we cannot find the side just by knowing the angle.

Insufficient.

Hence A.

Hope this helps.

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