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ABCD is a parallelogram. BD = 2. The angles of triangle BCD are all eq

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ABCD is a parallelogram. BD = 2. The angles of triangle BCD are all eq [#permalink]

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ABCD is a parallelogram. BD = 2. The angles of triangle BCD are all equal. What is the perimeter of the parallelogram?

A. 12
B. 9√3
C. 9
D. 8
E. 3√3

[Reveal] Spoiler:
Attachment:
p005-2.gif
p005-2.gif [ 691 Bytes | Viewed 3372 times ]
[Reveal] Spoiler: OA

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Re: ABCD is a parallelogram. BD = 2. The angles of triangle BCD are all eq [#permalink]

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New post 16 May 2016, 03:50
ABCD is a parallelogram. BD = 2. The angles of triangle BCD are all equal.

Triangle BCD is equilateral, so its side should also be equal
BD = BC= CD =2

Since ABCD is a parallelogram, opposite sides and angles should also be equal
Thus we have all sides of parallelogram ABCD = 2

Perimeter = 2 x 4 = 8
(Yes , this is a rhombus)

Correct option : D

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Re: ABCD is a parallelogram. BD = 2. The angles of triangle BCD are all eq [#permalink]

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New post 16 May 2016, 11:19
Bunuel wrote:
Image
ABCD is a parallelogram. BD = 2. The angles of triangle BCD are all equal. What is the perimeter of the parallelogram?

A. 12
B. 9√3
C. 9
D. 8
E. 3√3

[Reveal] Spoiler:
Attachment:
p005-2.gif


Quote:
The angles of triangle BCD are all equal and BD = 2


So, BC = BD = CD = BA = AD = 2

The parallelogram has 4 equal sides

BC = CD = BA = AD = 2

So The perimeter of the parallelogram will be 2*4 =8

Hence answer will be (D) 2
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Re: ABCD is a parallelogram. BD = 2. The angles of triangle BCD are all eq [#permalink]

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New post 16 May 2016, 13:05
Triangle BCD is an equilateral triangle. Which means all its sides are equal.

ABCD is a parallelogram, which means that all opposite sides are parallel and equal.

The 2 together imply that its a Rhombus with all sides of length 2.

Perimeter = 8. D


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ABCD is a parallelogram. BD = 2. The angles of triangle BCD are all eq [#permalink]

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New post 06 Jun 2016, 13:41
If all 3 angles of \(\triangle\) BCD are equal it means it is an equilateral \(\triangle\) and thus all its sides are equal
if 2 adjacent sides of parallelogram are equal it means that all sides are equal
AB=BC=CD=DA=2
perimeter of parallelogram = 4 * 2 = 8
Correct Answer - D

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Re: ABCD is a parallelogram. BD = 2. The angles of triangle BCD are all eq [#permalink]

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Re: ABCD is a parallelogram. BD = 2. The angles of triangle BCD are all eq   [#permalink] 18 Sep 2017, 12:06
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