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

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Math Expert
Joined: 02 Sep 2009
Posts: 55229
In the figure, what is the area of ∆ABC if EC/CD = 3 ?  [#permalink]

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02 Apr 2019, 23:38
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Difficulty:

55% (hard)

Question Stats:

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

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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

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#GREpracticequestion In the figure, what is the area.jpg [ 18.75 KiB | Viewed 475 times ]

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

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03 Apr 2019, 06:50
Bunuel wrote:

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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Joined: 25 Feb 2019
Posts: 279
Re: In the figure, what is the area of ∆ABC if EC/CD = 3 ?  [#permalink]

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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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Intern
Joined: 07 Feb 2019
Posts: 13
In the figure, what is the area of ∆ABC if EC/CD = 3 ?  [#permalink]

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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

Posted from my mobile device

How did you get AC = 27? More explanation needed.
Senior Manager
Joined: 25 Feb 2019
Posts: 279
Re: In the figure, what is the area of ∆ABC if EC/CD = 3 ?  [#permalink]

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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

Posted from my mobile device
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Joined: 19 Oct 2018
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Location: India
Re: In the figure, what is the area of ∆ABC if EC/CD = 3 ?  [#permalink]

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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
Intern
Joined: 29 Jan 2019
Posts: 3
Re: In the figure, what is the area of ∆ABC if EC/CD = 3 ?  [#permalink]

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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?
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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