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In the figure above, ABCD is a parallelogram.

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In the figure above, ABCD is a parallelogram. [#permalink] New post 16 Dec 2015, 04:52
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Attachment:
#GRepracticequestion In the figure above, ABCD is a parallelogram.jpg
#GRepracticequestion In the figure above, ABCD is a parallelogram.jpg [ 8.26 KiB | Viewed 1501 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
[Reveal] Spoiler: OA

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Re: figure above, ABCD is a parallelogram. [#permalink] New post 16 Dec 2015, 05:19
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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.
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Re: figure above, ABCD is a parallelogram. [#permalink] New post 29 Mar 2016, 09:01
Sandy, can you please attach a diagram with what you said please and label everything , thanks :)
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Re: figure above, ABCD is a parallelogram. [#permalink] New post 10 Apr 2016, 19:28
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This one's easy.

The formula for the area of a parallelogram is (base) x (height).

The height of this parallelogram (perpendicular distance to the top) is clearly less than 6, given the diagram (shortest distance between two points is a straight line / hypotenuse is the longest side of a triangle).

(<6)(4) = < 24

Choice B.
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Re: figure above, ABCD is a parallelogram. [#permalink] New post 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...
Image


...however, we don't know the height:
Image


However, if we recognize that we have a RIGHT TRIANGLE hiding in our diagram...
Image
... 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
Image
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

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Re: figure above, ABCD is a parallelogram.   [#permalink] 09 Feb 2019, 15:27
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In the figure above, ABCD is a parallelogram.

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