In the figure, what is the area of ∆ABC if EC/CD = 3 ? : Problem Solving (PS)

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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

Spoiler: ::

Attachment:

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

Spoiler: OA

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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

Spoiler: ::

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

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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, 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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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

award kudos if helpful

Posted from my mobile device

How did you get AC = 27? More explanation needed.

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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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21 Apr 2019, 20:30

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

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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

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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?