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08 May 2019, 01:57
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C
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Difficulty:
35%
(medium)
Question Stats:
77% (02:15) correct
23%
(01:46)
wrong
based on 69
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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
Attachment:
2019-05-08_1255.png [ 10.91 KiB | Viewed 2335 times ]
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
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
Vinit800HBS
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Joined: 29 Dec 2018
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GRE 1: Q170 V163
Expert reply
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
Posted from my mobile device
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
Posted from my mobile device
