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

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Math Expert
Joined: 02 Sep 2009
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ABCD is a parallelogram. BD = 2. The angles of triangle BCD are all eq [#permalink]

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16 May 2016, 02:38
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5% (low)

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94% (00:37) correct 6% (00:48) wrong based on 180 sessions

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

A. 12
B. 9√3
C. 9
D. 8
E. 3√3

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Posts: 79
Re: ABCD is a parallelogram. BD = 2. The angles of triangle BCD are all eq [#permalink]

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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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16 May 2016, 11:19
Bunuel wrote:

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

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

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

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18 Sep 2017, 12:06
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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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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