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In the figure above, ABCD is a parallelogram.
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16 Dec 2015, 04:52
16 Dec 2015, 04:52
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#GRepracticequestion In the figure above, ABCD is a parallelogram.jpg [ 8.26 KiB | Viewed 29824 times ]
In the figure above, ABCD is a parallelogram.
Quantity A |
Quantity B |
The area of ABCD |
24 |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Practice Questions
Question: 1
Page: 155
Difficulty: hard
Question: 1
Page: 155
Difficulty: hard
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In the figure above, ABCD is a parallelogram.
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09 Feb 2019, 15:27
09 Feb 2019, 15:27
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sandy wrote:
Attachment:
#GRepracticequestion In the figure above, ABCD is a parallelogram.jpg
In the figure above, ABCD is a parallelogram.
Quantity A |
Quantity B |
The area of ABCD |
24 |
The area of a parallelogram = (base)(height)
We know the base has length 4...
...however, we don't know the height:
However, if we recognize that we have a RIGHT TRIANGLE hiding in our diagram...
... we can use the fact that the hypotenuse is always the longest side in a RIGHT TRIANGLE.
Since the hypotenuse in the above triangle has length 6, we know that the other sides of the right triangle are LESS THAN 6
This means the triangle's height is less than 6
It also means the height of the parallelogram is less than 6
We're now ready to answer the question.
The area of a parallelogram = (base)(height)
= (4)(some number less than 6)
= some number less than 24
So, we get:
QUANTITY A: some number less than 24
QUANTITY B: 24
Answer: B
General Discussion
Re: figure above, ABCD is a parallelogram.
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16 Dec 2015, 05:19
16 Dec 2015, 05:19
3
Expert Reply
Solution
Here we parallelogram with sides 6 and 4.
Now from Geometry we know that area of parallelogram is base * height. Let 4 be the base and height be x. Suppose we draw a line from point B to AD perpendicular to AD. Say this perpendicular intersects at a point O with AD.
This triangle BAO is a right triangle with AB = 6 as its hypotenuse. Thus from property of right triangle AO = x; < AB = 6.
thus 4 * x < 4 *6
So Area of parallelogram < 24.
Hence Quantity B is greater.
Here we parallelogram with sides 6 and 4.
Now from Geometry we know that area of parallelogram is base * height. Let 4 be the base and height be x. Suppose we draw a line from point B to AD perpendicular to AD. Say this perpendicular intersects at a point O with AD.
This triangle BAO is a right triangle with AB = 6 as its hypotenuse. Thus from property of right triangle AO = x; < AB = 6.
thus 4 * x < 4 *6
So Area of parallelogram < 24.
Hence Quantity B is greater.
