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Which triangle, ADE or AEC, has the larger area? ABCD is a rectangle.

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Which triangle, ADE or AEC, has the larger area? ABCD is a rectangle. [#permalink]

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New post 22 Oct 2017, 06:44
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Which triangle, ADE or AEC, has the larger area? ABCD is a rectangle.

(1) DE is longer than EC.
(2) AC is longer than AE


[Reveal] Spoiler:
Attachment:
2017-10-22_1743.png
2017-10-22_1743.png [ 4.11 KiB | Viewed 471 times ]
[Reveal] Spoiler: OA

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Kudos [?]: 135295 [0], given: 12686

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Re: Which triangle, ADE or AEC, has the larger area? ABCD is a rectangle. [#permalink]

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New post 22 Oct 2017, 10:23
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Bunuel wrote:
Image
Which triangle, ADE or AEC, has the larger area? ABCD is a rectangle.

(1) DE is longer than EC.
(2) AC is longer than AE


[Reveal] Spoiler:
Attachment:
2017-10-22_1743.png


S1- DE>EC
Area of tr. ADE=\(\frac{1}{2}\) xDExAD
Area of tr. ACE=\(\frac{1}{2}\) xECxAD
Since DE>EC, Area of tr. ADE > Area of tr. ACE
Sufficient.

S2 - AC>AE.
Insufficient.

Answer A

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Re: Which triangle, ADE or AEC, has the larger area? ABCD is a rectangle. [#permalink]

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New post 23 Oct 2017, 14:38
Bunuel wrote:
Image
Which triangle, ADE or AEC, has the larger area? ABCD is a rectangle.

(1) DE is longer than EC.
(2) AC is longer than AE


[Reveal] Spoiler:
Attachment:
2017-10-22_1743.png


statement 1- DE>EC, sufficient. (Using formulae for triangle=1/2*base*height)
statement 2- insufficient.

Answer- A

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Re: Which triangle, ADE or AEC, has the larger area? ABCD is a rectangle. [#permalink]

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New post 23 Oct 2017, 17:30
1. As explained above, this relation is sufficient to compare the area.
2. This information is redundant. Diagonal will always be greater than AE (or other lengths). We need to know the ratio of the sides. Insufficient.

A

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Re: Which triangle, ADE or AEC, has the larger area? ABCD is a rectangle.   [#permalink] 23 Oct 2017, 17:30
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