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In the figure above, ABCD is a parallelogram. [#permalink]
16 Dec 2015, 04:52

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00:00

Question Stats:

69% (00:53) correct
30% (00:45) wrong based on 146 sessions

Attachment:

#GRepracticequestion In the figure above, ABCD is a parallelogram.jpg [ 8.26 KiB | Viewed 5514 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

Re: figure above, ABCD is a parallelogram. [#permalink]
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]
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]
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

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Re: In the figure above, ABCD is a parallelogram. [#permalink]
17 Jun 2020, 00:15

1

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A rectangle with the sides 6 and 4 would have an area of 24. If you distort it by dragging the top side with bottom side fixed, you decrease the height. Hence the area of this parallelogram is equivalent to a rectangle with a base 4 and height "lesser than 6", so the area is lesser than 24.

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Re: In the figure above, ABCD is a parallelogram.
[#permalink]
17 Jun 2020, 00:15