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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: 42338

Kudos [?]: 133141 [0], given: 12415

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

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12 Nov 2017, 10:22
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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

[Reveal] Spoiler:
Attachment:

2017-11-12_2103_001.png [ 6.06 KiB | Viewed 302 times ]
[Reveal] Spoiler: OA

_________________

Kudos [?]: 133141 [0], given: 12415

VP
Joined: 22 May 2016
Posts: 1003

Kudos [?]: 349 [0], given: 594

Re: ABCD is a parallelogram, and AED is an equilateral triangle. If C is [#permalink]

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12 Nov 2017, 14:03
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

[Reveal] Spoiler:
Attachment:
The attachment 2017-11-12_2103_001.png is no longer available

Attachment:

rrrrrrrrr.png [ 30.9 KiB | Viewed 143 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

Kudos [?]: 349 [0], given: 594

Re: ABCD is a parallelogram, and AED is an equilateral triangle. If C is   [#permalink] 12 Nov 2017, 14:03
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