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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
Posts: 58390
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)

Question Stats:

95% (00:59) correct 5% (01:36) wrong based on 234 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

Attachment:

p005-2.gif [ 691 Bytes | Viewed 2691 times ]

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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, 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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07 Oct 2018, 05:20
1
Bunuel wrote:

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

Dear Moderator,
Unable to see the image, please note I have not scrolled down, for fear of seeing the solution. Hope you will look into this and do the needful.
Thank you.
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- Stne
Math Expert
Joined: 02 Sep 2009
Posts: 58390
Re: ABCD is a parallelogram. BD = 2. The angles of triangle BCD are all eq  [#permalink]

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07 Oct 2018, 06:04
stne wrote:
Bunuel wrote:

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

Dear Moderator,
Unable to see the image, please note I have not scrolled down, for fear of seeing the solution. Hope you will look into this and do the needful.
Thank you.

________________
Fixed. Thank you.
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Re: ABCD is a parallelogram. BD = 2. The angles of triangle BCD are all eq   [#permalink] 07 Oct 2018, 06:04
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