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# ABCD is a parallelogram, and AED is an equilateral triangle. If C is

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Math Expert
Joined: 02 Sep 2009
Posts: 50627
ABCD is a parallelogram, and AED is an equilateral triangle. If C is  [#permalink]

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12 Nov 2017, 09:22
00:00

Difficulty:

15% (low)

Question Stats:

100% (01:21) correct 0% (00:00) wrong based on 30 sessions

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ABCD is a parallelogram, and AED is an equilateral triangle. If C is the midpoint of DE, and the perimeter of ∆AED is 12, what is the perimeter of ABCD?

(A) 16
(B) 14
(C) 12
(D) 10
(E) 9

Attachment:

2017-11-12_2103_001.png [ 6.06 KiB | Viewed 1124 times ]

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Joined: 22 May 2016
Posts: 2110
Re: ABCD is a parallelogram, and AED is an equilateral triangle. If C is  [#permalink]

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12 Nov 2017, 13:03
Bunuel wrote:

ABCD is a parallelogram, and AED is an equilateral triangle. If C is the midpoint of DE, and the perimeter of ∆AED is 12, what is the perimeter of ABCD?

(A) 16
(B) 14
(C) 12
(D) 10
(E) 9

Attachment:
The attachment 2017-11-12_2103_001.png is no longer available

Attachment:

rrrrrrrrr.png [ 30.9 KiB | Viewed 842 times ]

Find sides of $$\triangle$$ AED
AED is an equilateral triangle with perimeter of 12
Each side of $$\triangle$$ AED = $$\frac{12}{3} = 4$$
AD = DE = EA = 4

Find parallelogram side CD
C is the midpoint of DE
DE = 4, so CD = 2

Perimeter of parallelogram ABCD
Opposite sides of a parallelogram are equal
CD = AB = 2
Perimeter = 4 + 4 + 2 + 2 = 12

Re: ABCD is a parallelogram, and AED is an equilateral triangle. If C is &nbs [#permalink] 12 Nov 2017, 13:03
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