Angles /geometry

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nehakhas1: Senior | Next Rank: 100 Posts; Posts: 39; Joined: Wed Oct 15, 2008 11:25 amFollowed by: 1 member

by nehakhas1 » Sun Jul 05, 2009 3:24 pm

Each side of a certain parallelogram has length 6. if the area of the parallelogram is 18.
which of the following is the measure of one of its angles?
A. 30’ B. 45’ C. 60’ D. 90’ E.120’
Answer a

Please explain ..

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ssmiles08: Master | Next Rank: 500 Posts; Posts: 472; Joined: Sun Mar 29, 2009 6:54 pm; Thanked: 56 times

Re: Angles /geometry

by ssmiles08 » Sun Jul 05, 2009 3:44 pm

nehakhas1 wrote:Each side of a certain parallelogram has length 6. if the area of the parallelogram is 18.
which of the following is the measure of one of its angles?
A. 30’ B. 45’ C. 60’ D. 90’ E.120’
Answer a

Please explain ..

Area = b*h = 6*x = 18

x = 3. = height

the height is perpendicular to one of the sides. so if height = 3, hypotenuse = 6, base = 3sqrt(3) since they are 30-60-90 triangles.

the angle opposite to height(3) = 30 degrees.

(A)

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gmat740: MBA Student; Posts: 1194; Joined: Sat Aug 16, 2008 9:42 pmFollowed by: 17 members; Location: Paris, France; Thanked: 71 times; GMAT Score:710

by gmat740 » Sun Jul 05, 2009 9:28 pm

Hey there is a simple trigonometry formula for this

Area of parallelogram = a*b*(sin x)
where x= angle between the sides a and b

so, here a=b=6
and ar =18

6*6*(sin x) = 18
sin x= 0.5

and thus x= 30 degrees

Hope this helps

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shibal: Master | Next Rank: 500 Posts; Posts: 345; Joined: Wed Mar 18, 2009 6:53 pm; Location: Sao Paulo-Brazil; Thanked: 12 times; GMAT Score:660

by shibal » Tue Jul 07, 2009 6:07 pm

right, but it asks for 'one of its angles', therefore it could be 30,60,90.... how should we choose one of them in the test?

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gmat740: MBA Student; Posts: 1194; Joined: Sat Aug 16, 2008 9:42 pmFollowed by: 17 members; Location: Paris, France; Thanked: 71 times; GMAT Score:710

by gmat740 » Wed Jul 08, 2009 12:57 am

right, but it asks for 'one of its angles', therefore it could be 30,60,90.... how should we choose one of them in the test?

a GMAT question will have all the information required to get the answer. I don't feel like this is a good GMAT Question. It has to mention the angle between these two given sides.

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imhimanshu: Senior | Next Rank: 100 Posts; Posts: 87; Joined: Sat Feb 28, 2009 7:01 am; Location: India; Thanked: 2 times

by imhimanshu » Wed Jul 08, 2009 8:14 am

gmat740 wrote:
right, but it asks for 'one of its angles', therefore it could be 30,60,90.... how should we choose one of them in the test?
a GMAT question will have all the information required to get the answer. I don't feel like this is a good GMAT Question. It has to mention the angle between these two given sides.

me 2 agree and also getting 30 degrees as ansr.

Thanks

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Musiq: Senior | Next Rank: 100 Posts; Posts: 93; Joined: Thu Apr 10, 2008 1:42 pm; Location: Chicago; Thanked: 20 times

by Musiq » Wed Jul 08, 2009 8:28 am

shibal wrote:right, but it asks for 'one of its angles', therefore it could be 30,60,90.... how should we choose one of them in the test?

Shibal, the question is not asking for "Which of the following could be one of the angles in the TRIANGLE"?

The actual questions is " WHich of the following could be one of the angles in the PARALLELOGRAM?".

If one of the angles in the parallelogram is 30, then the other must necessarily be 150 degrees.

So, only 30 is the answer to this question.

For love, not money.

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Musiq: Senior | Next Rank: 100 Posts; Posts: 93; Joined: Thu Apr 10, 2008 1:42 pm; Location: Chicago; Thanked: 20 times

by Musiq » Wed Jul 08, 2009 8:32 am

gmat740 wrote:
right, but it asks for 'one of its angles', therefore it could be 30,60,90.... how should we choose one of them in the test?
a GMAT question will have all the information required to get the answer. I don't feel like this is a good GMAT Question. It has to mention the angle between these two given sides.

Could you please explain why the angle between these 2 given sides MUST be mentioned?

The problem clearly asks for one of the angles of the parallelogram and not the triangle.

For love, not money.

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Musiq: Senior | Next Rank: 100 Posts; Posts: 93; Joined: Thu Apr 10, 2008 1:42 pm; Location: Chicago; Thanked: 20 times

by Musiq » Wed Jul 08, 2009 8:36 am

If anything, Trig is very NON-GMAT; though it is extremely time-saving to use for someone who already knows the basic ratios.

The reason this is a valid GMAT problem ,in my opinion, is that it uses special right angles ratios.

There are 2 important ratios to always remember for right angles:
A) In a 90 - 45- 45 triangle, the ratio of the corresponding sides is SQRT2 : 1: 1
B) In a 90 - 60 - 30 triangle, the ratio of the corresponding sides is 2: SQRT3:1.

So, when we see that the Right triangle created by the Height and the Base of this parallelogram have sides 3 and 6 respectively ( 3 is derived from the Area = 18), we identify a Right triangle with the ratio 2:1.

Therefore, it MUST be a 90-60-30 triangle...hence the OA = 30.

For love, not money.

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