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In the figure, what is the area of ∆ABC if EC/CD = 3 ?

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Joined: 02 Sep 2009
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In the figure, what is the area of ∆ABC if EC/CD = 3 ?  [#permalink]

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New post 02 Apr 2019, 23:38
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

62% (02:56) correct 38% (03:09) wrong based on 42 sessions

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CEO
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Joined: 18 Aug 2017
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Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
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Re: In the figure, what is the area of ∆ABC if EC/CD = 3 ?  [#permalink]

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New post 03 Apr 2019, 06:50
Bunuel wrote:
Image
In the figure, what is the area of \(∆ABC\) if \(\frac{EC}{CD} = 3\) ?

(A) 12

(B) 24

(C) 81

(D) 121.5

(E) 143


Attachment:
#GREpracticequestion In the figure, what is the area.jpg



IMO ∆EDC ~ ∆ABC
area of ∆EDC= 1/2 * 12* 4 ; 24
so IMO B
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Re: In the figure, what is the area of ∆ABC if EC/CD = 3 ?  [#permalink]

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New post 03 Apr 2019, 07:02
IMO D

triangle ABC and EDC are congruent

so the ratio of corresponding sides will be equal .

we get AC = 27

area = 1/2*27*9 = 121.5


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In the figure, what is the area of ∆ABC if EC/CD = 3 ?  [#permalink]

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New post 21 Apr 2019, 16:46
m1033512 wrote:
IMO D

triangle ABC and EDC are congruent

so the ratio of corresponding sides will be equal .

we get AC = 27

area = 1/2*27*9 = 121.5


award kudos if helpful

Posted from my mobile device


How did you get AC = 27? More explanation needed.
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Re: In the figure, what is the area of ∆ABC if EC/CD = 3 ?  [#permalink]

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New post 21 Apr 2019, 20:30
1
from Ec/CD = 3 and EC = 12
we get CD = 4

now in similar triangle abc and edc

EC/AC= CD/BC


put the values, you will get AC = 27


award kudos if helpful

Posted from my mobile device
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Re: In the figure, what is the area of ∆ABC if EC/CD = 3 ?  [#permalink]

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New post 21 Apr 2019, 22:43
tanx=EC/CD=AC/BC
3=AC/9
OR AC=27
Area of ABC=0.5*27*9=121.5
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Re: In the figure, what is the area of ∆ABC if EC/CD = 3 ?  [#permalink]

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New post 24 Apr 2019, 07:19
m1033512 wrote:
from Ec/CD = 3 and EC = 12
we get CD = 4

now in similar triangle abc and edc

EC/AC= CD/BC

put the values, you will get AC = 27
Posted from my mobile device

How are abc and edc similar?
GMAT Club Bot
Re: In the figure, what is the area of ∆ABC if EC/CD = 3 ?   [#permalink] 24 Apr 2019, 07:19
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In the figure, what is the area of ∆ABC if EC/CD = 3 ?

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