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Quantitative Revision from Richa Q #3

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by richachampion » Sat Nov 12, 2016 12:38 am
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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by richachampion » Sat Nov 12, 2016 12:48 am
Theorem: In a 30°-60°-90° triangle the sides are in the ratio 1 : 2 : √3
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by Jay@ManhattanReview » Mon Dec 12, 2016 10:33 pm
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
Just to conclude it to the answer...

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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by melguy » Tue Dec 13, 2016 8:14 pm
Jay@ManhattanReview wrote:
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
Just to conclude it to the answer...

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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30-60-90.JPG
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by Jay@ManhattanReview » Tue Dec 13, 2016 8:26 pm
melguy wrote:
Jay@ManhattanReview wrote:
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
Just to conclude it to the answer...

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?)
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.

Thus, area = 6*2 = 12

OA: B

-Jay

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