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# If the area of parallelogram ABCD is 16*3^(1/2), what is the

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If the area of parallelogram ABCD is 16*3^(1/2), what is the [#permalink]

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24 Sep 2013, 23:59
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parallelogram.jpg [ 6.76 KiB | Viewed 2238 times ]
If the area of parallelogram ABCD is $$16\sqrt{3}$$, what is the length of BD?

A. $$2$$
B. $$2\sqrt{3}$$
C. $$6$$
D. $$4\sqrt{3}$$
E. $$8$$
[Reveal] Spoiler: OA

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Collection of some good questions on Number System

Last edited by Bunuel on 25 Sep 2013, 01:06, edited 1 time in total.
Edited the question.

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Re: If the area of parallelogram ABCD is 16*3^(1/2), what is the [#permalink]

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25 Sep 2013, 01:25
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TirthankarP wrote:
Attachment:
The attachment parallelogram.jpg is no longer available
If the area of parallelogram ABCD is $$16\sqrt{3}$$, what is the length of BD?

A. $$2$$
B. $$2\sqrt{3}$$
C. $$6$$
D. $$4\sqrt{3}$$
E. $$8$$

Drop the height from angle B:
Attachment:

Untitled.png [ 12.08 KiB | Viewed 2209 times ]
ABE is 30-60-90 right triangle. The sides are in the ratio $$1:\sqrt{3}:2$$. Since given that hypotenuse AB = 4, then AE (the smalles side) is 2, and BE is $$2\sqrt{3}$$.

The area of a parallelogram is height*base, thus $$BE*AD=2\sqrt{3}*AD =16\sqrt{3}$$ --> AD=8.

Next, ED = AD - AE = 8 - 2 = 6.

Finally, $$BD =\sqrt{BE^2+ED^2}=\sqrt{12+36}=4\sqrt{3}$$.

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Re: If the area of parallelogram ABCD is 16*3^(1/2), what is the [#permalink]

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01 Nov 2017, 08:20
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Re: If the area of parallelogram ABCD is 16*3^(1/2), what is the   [#permalink] 01 Nov 2017, 08:20
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