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

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

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New post 04 Oct 2017, 11:13
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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
2017-10-04_1123_002.png [ 8.04 KiB | Viewed 1425 times ]

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

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New post 04 Oct 2017, 11:29
1
Bunuel wrote:
Image
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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New post 04 Oct 2017, 11:39
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

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

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New post 03 Nov 2017, 11:58
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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New post 03 Nov 2017, 19:41
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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New post 03 Nov 2017, 20:28
I can't work out 24 either. My answer is A like many of you. Awaiting for the OA.
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Re: In the figure above, if the perimeter of quadrilateral ABCD is 24, wha  [#permalink]

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New post 03 Nov 2017, 20:42
1
Bunuel wrote:
Image
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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Re: In the figure above, if the perimeter of quadrilateral ABCD is 24, wha  [#permalink]

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New post 03 Nov 2017, 23:35
chetan2u wrote:
Bunuel wrote:
Image
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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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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

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New post 04 Nov 2017, 08:45
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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Re: In the figure above, if the perimeter of quadrilateral ABCD is 24, wha  [#permalink]

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New post 17 Nov 2017, 03:36
Question needs more information because given information doesn't means neither that AD II BC nor AB is perpendicular to AD.
Provided information is not sufficient to reach at answer.
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Re: In the figure above, if the perimeter of quadrilateral ABCD is 24, wha  [#permalink]

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New post 17 Nov 2017, 04:31
gvij2017 wrote:
Question needs more information because given information doesn't means neither that AD II BC nor AB is perpendicular to AD.
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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Re: In the figure above, if the perimeter of quadrilateral ABCD is 24, wha &nbs [#permalink] 17 Nov 2017, 04:31
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