In parallelogram PQRS shown, if PQ = 4 and QR = 6, what is the area of PQRS?
A. 8
B. 12
C. 24
D. 8√3
E. 12√3
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Quantitative Revision from Richa Q #3
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richachampion
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richachampion
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Theorem: In a 30°-60°-90° triangle the sides are in the ratio 1 : 2 : √3
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Jay@ManhattanReview
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Just to conclude it to the answer...richachampion wrote:In parallelogram PQRS shown, if PQ = 4 and QR = 6, what is the area of PQRS?
A. 8
B. 12
C. 24
D. 8√3
E. 12√3
We know that area of a parallelogram = Base * Height;
We are given that Base = 6; however, the Height is not given.
We know that in a 30°-60°-90° triangle, the sides are in the ratio 1 : 2 : √3, respectively.
Thus, the side opposite to 90° = PQ = 4 => the side opposite to 30° = Height = 4/√3
=> Area of a parallelogram = Base * Height = 6 * 4/√3 = 24/√3 = 12√3
OA: E
Hope this helps!
-Jay
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melguy
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Jay@ManhattanReview wrote:Just to conclude it to the answer...richachampion wrote:In parallelogram PQRS shown, if PQ = 4 and QR = 6, what is the area of PQRS?
A. 8
B. 12
C. 24
D. 8√3
E. 12√3
We know that area of a parallelogram = Base * Height;
We are given that Base = 6; however, the Height is not given.
We know that in a 30°-60°-90° triangle, the sides are in the ratio 1 : 2 : √3, respectively.
Thus, the side opposite to 90° = PQ = 4 => the side opposite to 30° = Height = 4/√3
=> Area of a parallelogram = Base * Height = 6 * 4/√3 = 24/√3 = 12√3
OA: E
Hope this helps!
-Jay
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Manhattan guide suggest that 30°-60°-90° ratio is 1 : √3 : 2. Based on that the height should become 2.
Base x Height = 6 x 2 = 12 (unless the 30° angle is incorrectly mentioned in the figure?)
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Jay@ManhattanReview
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Yes, it is correct. For a 30°-60°-90° triangle, the sides are in the ratio 1 : √3 : 2, respectively. In that case, the height should be 2.melguy wrote:Jay@ManhattanReview wrote:Just to conclude it to the answer...richachampion wrote:In parallelogram PQRS shown, if PQ = 4 and QR = 6, what is the area of PQRS?
A. 8
B. 12
C. 24
D. 8√3
E. 12√3
We know that area of a parallelogram = Base * Height;
We are given that Base = 6; however, the Height is not given.
We know that in a 30°-60°-90° triangle, the sides are in the ratio 1 : 2 : √3, respectively.
Thus, the side opposite to 90° = PQ = 4 => the side opposite to 30° = Height = 4/√3
=> Area of a parallelogram = Base * Height = 6 * 4/√3 = 24/√3 = 12√3
OA: E
Hope this helps!
-Jay
_________________
Manhattan Review GMAT Prep
Locations: New York | Bangkok | Abu Dhabi | Rome | and many more...
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Manhattan guide suggest that 30°-60°-90° ratio is 1 : √3 : 2. Based on that the height should become 2.
Base x Height = 6 x 2 = 12 (unless the 30° angle is incorrectly mentioned in the figure?)
Thus, area = 6*2 = 12
OA: B
-Jay
_________________
Manhattan Review GMAT Prep
Locations: New York | Singapore | Doha | Lausanne | and many more...
Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.[spoiler][/spoiler]
