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A triangle ABC has points D and E which lie on sides AB and AC respect

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A triangle ABC has points D and E which lie on sides AB and AC respect  [#permalink]

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New post 28 Jun 2018, 10:27
2
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

44% (01:43) correct 56% (02:15) wrong based on 24 sessions

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A triangle ABC has points D and E which lie on sides AB and AC respectively. Length of AD is 6 units and length of EC is 3 units. What is the length of AE?

(1) If points D and E are joined to each other, line DE will be parallel to side BC of triangle ABC.

(2) Length of BD is 2 units.
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Re: A triangle ABC has points D and E which lie on sides AB and AC respect  [#permalink]

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New post 04 Jul 2018, 20:16
amanvermagmat wrote:
A triangle ABC has points D and E which lie on sides AB and AC respectively. Length of AD is 6 units and length of EC is 3 units. What is the length of AE?

(1) If points D and E are joined to each other, line DE will be parallel to side BC of triangle ABC.

(2) Length of BD is 2 units.


Given, AD=6 unit, EC=3 unit

Question stem, AE=?

Property:-

Any line parallel to one side of a triangle divides the other two sides proportionally.


Statement-1
Here, DE is drawn parallel to BC, it would divide sides AB and AC proportionally, i.e.,
\(\frac{AD}{DB}\)=\(\frac{AE}{EC}\)
Or, \(\frac{6}{DB}\)=\(\frac{AE}{3}\)-----------------(1)
We can't find the length of AE as the length of DB is not known.
Hence, insufficient.

Statement-2
Given, BD=2 unit, So what? No other relevant info is available.(No info on the positioning of D & E)

Clearly, insufficient.

Now combining st1 & st2, we have from (1),
\(\frac{6}{DB}\)=\(\frac{AE}{3}\)(substituting the value of BD from st2)
Or,\(\frac{6}{2}=\frac{AE}{3}\)
Or,3=\(\frac{AE}{3}\)
Or, AE=9 unit


Clearly sufficient,though the highlighted portion needn't to be computed,

Diagram affixed for reference.(Not to scale)

Ans. C
Attachments

Triangle.JPG
Triangle.JPG [ 24.53 KiB | Viewed 391 times ]


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PKN

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Re: A triangle ABC has points D and E which lie on sides AB and AC respect &nbs [#permalink] 04 Jul 2018, 20:16
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