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

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Math Expert
Joined: 02 Sep 2009
Posts: 50627
Which triangle, ADE or AEC, has the larger area? ABCD is a rectangle.  [#permalink]

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22 Oct 2017, 05:44
00:00

Difficulty:

35% (medium)

Question Stats:

76% (01:28) correct 24% (01:33) wrong based on 49 sessions

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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

Attachment:

2017-10-22_1743.png [ 4.11 KiB | Viewed 776 times ]

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

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22 Oct 2017, 09:23
1
Bunuel wrote:

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

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.

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Joined: 22 May 2017
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Re: Which triangle, ADE or AEC, has the larger area? ABCD is a rectangle.  [#permalink]

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23 Oct 2017, 13:38
Bunuel wrote:

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

Attachment:
2017-10-22_1743.png

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

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

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23 Oct 2017, 16:30
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
Re: Which triangle, ADE or AEC, has the larger area? ABCD is a rectangle. &nbs [#permalink] 23 Oct 2017, 16:30
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