The Logical approach to this question will start off with the understanding that since both triangles are regular triangles which share one equal leg (the width of the rectangle), all we need in order to find the ratio between their areas is to find the ratio between their other legs. Statement (1) doesn't relate to AE and EB, but statement (2) does - so the correct answer is (B).

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\(area \ of \ EDA=\frac{1}{2}*AD*AE\)
\(area \ of \ EBC=\frac{1}{2}*BC*BE\)

RATIO =\(\frac{1}{2}*AD*AE/\frac{1}{2}*BC*BE.\) BUT \(AD=BC\), SO RATIO IS \(\frac{AE}{BE}\).
WHICH STATEMENT 2 PROVIDES. imo, OPTION b.

Let \(w\) be the width of the rectangle. The original question: \(\frac{\frac{AE\cdot w}{2}}{\frac{EB\cdot w}{2}}=\frac{AE}{EB}=?\)

1) We know that \(w=4\), but no information is given about \(AE\) or \(EB\). Thus, we can't get a unique value to answer the original question. \(\implies\) Insufficient

2) We know that \(AE=2\) and \(EB=4\), so \(\frac{AE}{EB}=\frac{2}{4}=\frac{1}{2}\). Thus, the answer to the original question is a unique value. \(\implies\) Sufficient

Answer: B
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Hi All,

We're told that in the figure above, ABCD is a rectangular region. We're asked for the value of the ratio of (area of triangle EDA)/(area of triangle EBC)? This question is based on a couple of Geometry rules. It's worth noting that all 3 triangles (EDA, EBC and EDC) all have the SAME height (so the height of the triangles is actually IRRELEVENT to the question that is asked - as that number will 'cancel out' in the numerator and denominator of the fraction). Thus we ultimately need to know how the two 'bases' of EDA and EBC relate to one another to answer this question.

(1) AD = 4

Fact 1 gives us the height of the triangles, but that does not impact the question at all. The calculation would be:
(1/2)(Base of EDA)(4) / (1/2)(Based of EBC)(4) = ?
(Base of EDA) / (Base of EBC) = ?
Fact 1 is INSUFFICIENT

(2) AE = 2 and EB = 4

Fact 2 gives us the exact lengths of the two 'bases' - and that's all we need to answer the question. The answer would be 2/4 = 1/2
Fact 2 is SUFFICIENT

Final Answer:

GMAT assassins aren't born, they're made,
Rich
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We are finding the area, so we just need 1/2 BH.
They both share the same H so we just need to figure out the Base.
In 1) We are given the H, no thank you GMAT (this won't help us)
2) They give us 2 bases, well if the triangles share the same height then we can just compare the bases. Suff (B)
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Wanted: AE/EB?
Height doesn't matter since it cancelled out as it's the same for both

1) Not sufficient

2) Sufficient