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If, in the figure above, ABCD is a rectangular region, what is the val

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If, in the figure above, ABCD is a rectangular region, what is the val  [#permalink]

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26 Apr 2019, 03:04
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If, in the figure above, ABCD is a rectangular region, what is the value of the ratio $$\frac{area \ of \ EDA}{area \ of \ EBC}$$ ?

(2) AE = 2 and EB = 4

DS34602.01
OG2020 NEW QUESTION

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2019-04-26_1401.png [ 7.91 KiB | Viewed 657 times ]

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Re: If, in the figure above, ABCD is a rectangular region, what is the val  [#permalink]

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26 Apr 2019, 15:02
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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Re: If, in the figure above, ABCD is a rectangular region, what is the val  [#permalink]

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26 Apr 2019, 15:14
Bunuel wrote:
If, in the figure above, ABCD is a rectangular region, what is the value of the ratio $$\frac{area \ of \ EDA}{area \ of \ EBC}$$ ?

(2) AE = 2 and EB = 4

DS34602.01
OG2020 NEW QUESTION

Attachment:
2019-04-26_1401.png

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

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.
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Re: If, in the figure above, ABCD is a rectangular region, what is the val  [#permalink]

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27 Apr 2019, 19:55
1
Bunuel wrote:

If, in the figure above, ABCD is a rectangular region, what is the value of the ratio $$\frac{area \ of \ EDA}{area \ of \ EBC}$$ ?

(2) AE = 2 and EB = 4

DS34602.01
OG2020 NEW QUESTION

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

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Re: If, in the figure above, ABCD is a rectangular region, what is the val  [#permalink]

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12 May 2019, 14:13
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.

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

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Re: If, in the figure above, ABCD is a rectangular region, what is the val   [#permalink] 12 May 2019, 14:13
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