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What is the area of triangle EBC?

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What is the area of triangle EBC? [#permalink]

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What is the area of triangle EBC?

(1) The area of ΔAED is 16.

(2) The area of ΔDEC is 12.

[Reveal] Spoiler:
Attachment:
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[Reveal] Spoiler: OA

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Re: What is the area of triangle EBC? [#permalink]

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New post 17 Sep 2010, 02:35
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rafi wrote:
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What is the area of triangle EBC?

(1) The area of ΔAED is 16.

(2) The area of ΔDEC is 12.

How do you solve this question?


Note that area of ADC and BDC is the same (common base and and since AB is parallel to CD, same perpendicular distance to base CD from A and B)

Area(BEC) = Area(BDC) - Area(EDC)
Area(AED) = Area(ADC) - Area(EDC)
=> Area(BEC)=Area(AED)

(1) --> Clearly sufficient
(2) --> Not sufficient, there is no relationship between Area(EDC) and Area(BEC) directly, without any extra knowledge
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Re: What is the area of triangle EBC? [#permalink]

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New post 09 Jul 2016, 12:30
Hello from the GMAT Club BumpBot!

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What is the area of triangle EBC? [#permalink]

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New post 27 Jul 2016, 19:07
Since it took me a long time to understand the above reply (kudos given), my clarification:

\(\text{Area of a Triangle}: \frac{1}{2} \times \text{base} \times \text{height}\)
\(ADC\) and \(BDC\) share a base (\(DC\)).
\(ADC\) and \(BDC\) have the same height as we can determine \(AD\) and \(BC\) are parallel (due to the two right angles).

Therefore areas of \(ADC\) and \(BDC\) are equal.

(1) The area of ΔAED is 16.

The area of ADC = BDC (given above).
Using visual area subtraction
AED = ADC - DEC
BEC = BDC - DEC

Therefore the area of AED = BEC.

Sufficient

(2) The area of ΔDEC is 12.

This information cannot be used to obtain anything more as we cannot determine side lengths or angles from the information.

Insufficient

[Reveal] Spoiler:
(A) statement 1 alone is sufficient, but statement 2 alone is not sufficient to answer the question

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Re: What is the area of triangle EBC? [#permalink]

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New post 28 Jul 2016, 02:48
Very good question. This forum is superb.

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Re: What is the area of triangle EBC? [#permalink]

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New post 26 Sep 2017, 19:41
Hello from the GMAT Club BumpBot!

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Re: What is the area of triangle EBC?   [#permalink] 26 Sep 2017, 19:41
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