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# In the figure above, if the perimeter of quadrilateral ABCD is 24, wha

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Math Expert
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Posts: 52108
In the figure above, if the perimeter of quadrilateral ABCD is 24, wha  [#permalink]

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04 Oct 2017, 10:13
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Difficulty:

55% (hard)

Question Stats:

80% (02:27) correct 20% (02:33) wrong based on 128 sessions

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In the figure above, if the perimeter of quadrilateral ABCD is 24, what is the area of ∆ ECD?

(A) 12
(B) 15
(C) 20
(D) 24
(E) 30

Attachment:

2017-10-04_1123_002.png [ 8.04 KiB | Viewed 1543 times ]

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Re: In the figure above, if the perimeter of quadrilateral ABCD is 24, wha  [#permalink]

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04 Oct 2017, 10:29
1
Bunuel wrote:

In the figure above, if the perimeter of quadrilateral ABCD is 24, what is the area of ∆ ECD?

(A) 12
(B) 15
(C) 20
(D) 24
(E) 30

Attachment:
2017-10-04_1123_002.png

As $$BC || AD$$, angle $$BCE=CED=x°$$. Hence triangle $$ECD$$ is isosceles with $$CE=CD=5$$

Given perimeter of $$ABCD=24$$, so $$AD=24-(3+6+5)=10$$

$$ED=AD-AE=10-2=8$$

Height of triangle $$ECD = AB = 3$$ and Base $$ED=8$$

So area $$= \frac{1}{2}*3*8=12$$

Option A
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Re: In the figure above, if the perimeter of quadrilateral ABCD is 24, wha  [#permalink]

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04 Oct 2017, 10:39
1
As BC is parallel to AD, Angle BCE = Angle CED = X

Since Angles BCE & CED are equal, Triangle ECD is isosceles, therefore CD = EC = 5

Perimeter of ABCD = AB + BC + CD + AE + ED = 3 + 6 + 5 + 2 + ED = 24 ==> ED = 8

Height of Triangle ECD is 3

Area of Triangle ECD = $$\frac{1}{2}$$ * 8 * 3 = 12

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Joined: 01 May 2017
Posts: 4
Re: In the figure above, if the perimeter of quadrilateral ABCD is 24, wha  [#permalink]

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03 Nov 2017, 10:58
Bunuel can you explain how 24?
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Re: In the figure above, if the perimeter of quadrilateral ABCD is 24, wha  [#permalink]

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03 Nov 2017, 18:41
bara25 wrote:
Bunuel can you explain how 24?

Hi Bunuel

I agree with bara25. Kindly provide the OA or can you highlight the errors in my approach. IMO answer should be 12
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Re: In the figure above, if the perimeter of quadrilateral ABCD is 24, wha  [#permalink]

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03 Nov 2017, 19:28
I can't work out 24 either. My answer is A like many of you. Awaiting for the OA.
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Joined: 02 Aug 2009
Posts: 7199
Re: In the figure above, if the perimeter of quadrilateral ABCD is 24, wha  [#permalink]

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03 Nov 2017, 19:42
1
Bunuel wrote:

In the figure above, if the perimeter of quadrilateral ABCD is 24, what is the area of ∆ ECD?

(A) 12
(B) 15
(C) 20
(D) 24
(E) 30

Attachment:
2017-10-04_1123_002.png

hi Bunuel
there seems to be some typo..
Either the answer is for AREA of trapezium ABCD.. then it is 24
or typo in OA, as ans should be 12
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Joined: 02 Sep 2009
Posts: 52108
Re: In the figure above, if the perimeter of quadrilateral ABCD is 24, wha  [#permalink]

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03 Nov 2017, 22:35
chetan2u wrote:
Bunuel wrote:

In the figure above, if the perimeter of quadrilateral ABCD is 24, what is the area of ∆ ECD?

(A) 12
(B) 15
(C) 20
(D) 24
(E) 30

Attachment:
2017-10-04_1123_002.png

hi Bunuel
there seems to be some typo..
Either the answer is for AREA of trapezium ABCD.. then it is 24
or typo in OA, as ans should be 12

The OA is A. Edited. Sorry for that.
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Re: In the figure above, if the perimeter of quadrilateral ABCD is 24, wha  [#permalink]

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04 Nov 2017, 07:45
darn it:)) I killed myself yesterday, solved for A in 1 min, the OA was 24, and spent like 1h trying to figure out how the hell on earth that can be 24 ) solved like in 3 different way, 12 again
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Posts: 289
Re: In the figure above, if the perimeter of quadrilateral ABCD is 24, wha  [#permalink]

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17 Nov 2017, 02:36
Provided information is not sufficient to reach at answer.
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Posts: 7199
Re: In the figure above, if the perimeter of quadrilateral ABCD is 24, wha  [#permalink]

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17 Nov 2017, 03:31
gvij2017 wrote:
Provided information is not sufficient to reach at answer.

Hi..
It is clearly given that AB is perpendicular to AD by showing sign of L at the angle. A squarish box at the angle tells us that angle is 90..
Also if two sides on the base are 90°, the two sides will be perpendicular since both are at same angle.

Seems you are misunderstanding something
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: In the figure above, if the perimeter of quadrilateral ABCD is 24, wha &nbs [#permalink] 17 Nov 2017, 03:31
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