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In the diagram above, ABCD is a parallelogram with an area of 96 squar

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Bunuel
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In the diagram above, ABCD is a parallelogram with an area of 96 squar [#permalink] New post   08 May 2019, 01:57
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In the diagram above, ABCD is a parallelogram with an area of 96 square inches. If CD has a length of 8 inches and ∠B measures 120°, what is the length of BC?

A. 10
B. 12
C. \(8\sqrt{3}\)
D. \(10 \sqrt{3}\)
E. 18


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C
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Re: In the diagram above, ABCD is a parallelogram with an area of 96 squar [#permalink] New post   08 May 2019, 05:04
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Concepts to use . . .
1. Opposite angles of a parallelogram are same.
2. Sides of 30-60-90 right-angled triangle are in ratio 1:√3:2

Let us extend the side AD and draw a perpendicular to the extended side from a point C so that we can form a right-angled triangle.

Using concept 1 as mentioned above, we can find out that the angle adjacent to angle ADC is 60*
So, the right angle is a special 30-60-90 triangle.

We know that side opposite to 90* is 8 so the side opposite to 60* would be 4√3

So, the height of ||gram = 4√3
It is given that the area of ||gram = base x height = 96
So, BC x 4√3 = 96
BC=8√3

Correct C 8√3
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Re: In the diagram above, ABCD is a parallelogram with an area of 96 squar [#permalink] New post   08 May 2019, 05:26
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Knowledge of few additional formulas can really work wonders.

Area of a parallelogram = Product Of two adjacent sides * Sine of angle between them

Here, Area = 8*BC*Sin(60) = 96
Sin(60) = Root(3)/2
BC = 8 root (3)

Option C

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Re: In the diagram above, ABCD is a parallelogram with an area of 96 squar [#permalink] New post   12 May 2019, 19:12
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Bunuel wrote:

In the diagram above, ABCD is a parallelogram with an area of 96 square inches. If CD has a length of 8 inches and ∠B measures 120°, what is the length of BC?

A. 10
B. 12
C. \(8\sqrt{3}\)
D. \(10 \sqrt{3}\)
E. 18

Show Spoiler
Attachment:
2019-05-08_1255.png



Since angle B is 120, then angle D = 120 and angle A = angle C = 60.

We see that if we drop a height from angle B to side AD, we now have a 30-60-90 right triangle with a hypotenuse AB = 8. Thus, the height, which is opposite angle A is 4√3. Since the area is 96, the base is:

96/(4√3) = 24/√3 = 24√3/3 = 8√3

Answer: C
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Re: In the diagram above, ABCD is a parallelogram with an area of 96 squar [#permalink]
12 May 2019, 19:12
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