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ketkoag: Legendary Member; Posts: 876; Joined: Thu Apr 10, 2008 8:14 am; Thanked: 13 times

angle

by ketkoag » Wed May 06, 2009 10:44 am

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’

OA: A , but if A is the answer then why not E . try to draw a parallelogram with all sides equal and if one angle is 30 then the other angle has to be 120.

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Source: Beat The GMAT — Problem Solving | Wed May 06, 2009 10:44 am

mike22629: Master | Next Rank: 500 Posts; Posts: 322; Joined: Fri Mar 27, 2009 3:56 pm; Thanked: 24 times; GMAT Score:710

by mike22629 » Wed May 06, 2009 10:50 am

30 + 30 + 120 +120 = 300 (not 360)

Other side would be 150

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m&m: Master | Next Rank: 500 Posts; Posts: 134; Joined: Sun Feb 15, 2009 7:44 pm; Thanked: 14 times

by m&m » Wed May 06, 2009 5:23 pm

it say "what is measure of one of the angles". So we know the angles all add to 360 - so if any 2 answers add to 180 then it must be wrong since there would be 2 possible angles choices in the answers.

E & C must then be eliminated
also D cannot be because then we would have a square
so if you had to guess you just made your chances of success 50%

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gauravgundal: Master | Next Rank: 500 Posts; Posts: 199; Joined: Mon Apr 06, 2009 4:15 am; Location: India; Thanked: 13 times

by gauravgundal » Thu May 07, 2009 3:10 am

Answer: A
Area of Parallelogram = Base * height
18 = 6 * h
h=3

consider a llm with 6 as side and draw a height of 3
the angle associated with the height and side of 6 is angle 30

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Pranay: Senior | Next Rank: 100 Posts; Posts: 59; Joined: Tue May 05, 2009 1:58 am; Thanked: 1 times

by Pranay » Thu May 07, 2009 5:25 am

gauravgundal wrote:Answer: A
Area of Parallelogram = Base * height
18 = 6 * h
h=3

consider a llm with 6 as side and draw a height of 3
the angle associated with the height and side of 6 is angle 30

Hi Gaurav,

Pranay .. again.

Could you please explain the last step associated with conclusion of angle being 30 degrees.

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hk: MBA Student; Posts: 532; Joined: Wed Jan 28, 2009 1:39 pm; Location: Barcelona; Thanked: 33 times; Followed by:9 members; GMAT Score:640

by hk » Thu May 07, 2009 9:50 am

Pranay,

The area of the parallelogram = b*h
18=6*h
h=3

Now drop a line from one of the top edges to the base. you will for a right angle triangle. with h=3, hypotenuse=6 and let x be the other side.

solving we get x=3 Sqrt(3)

This forms a 1:sqrt(3):2 (which have angles 90,60 and 30) triangle and the angle opposite to the smallest side which is 3, is 30' and happens to be one side of the parallelogram. Do not fall into the trap and choose 60 because this just forms a part of the angle. (See diagram)

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