Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 26 Jun 2007
Posts: 104

Each side of a certain parallelogram has length 6. If the area of the [#permalink]
Show Tags
26 Jan 2008, 11:31
1
This post received KUDOS
18
This post was BOOKMARKED
Question Stats:
52% (01:35) correct 48% (01:22) wrong based on 434 sessions
HideShow timer Statistics
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
Official Answer and Stats are available only to registered users. Register/ Login.



Manager
Joined: 01 Sep 2007
Posts: 98
Location: Astana

Re: Each side of a certain parallelogram has length 6. If the area of the [#permalink]
Show Tags
26 Jan 2008, 11:48
Since it is a PS question, I would pick D on exam. sides are equal so it most probably a rhomb. if i recall correctly, the area of a rhomb is half the product of its diagonals? d1d2 = 18*2 = 36. perhaps diagonals are equal in lenght (sqrt 36 = 6).
so we have two equilateral traingles. where angles are equal to 60 degrees.



CEO
Joined: 17 Nov 2007
Posts: 3525
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth)  Class of 2011

Re: Each side of a certain parallelogram has length 6. If the area of the [#permalink]
Show Tags
26 Jan 2008, 12:44
7
This post received KUDOS
Expert's post
2
This post was BOOKMARKED
AArea=h*a 18=6*h ==> h=3
Attachments
t59092.gif [ 13.92 KiB  Viewed 8040 times ]
_________________
HOT! GMAT TOOLKIT 2 (iOS) / GMAT TOOLKIT (Android)  The OFFICIAL GMAT CLUB PREP APP, a musthave app especially if you aim at 700+  PrepGame



Senior Manager
Joined: 22 Sep 2005
Posts: 273

Re: Each side of a certain parallelogram has length 6. If the area of the [#permalink]
Show Tags
26 Jan 2008, 13:50
1
This post received KUDOS
A too.
We know that Area= base * height. If the Area=18, and base = 6, height must be 3, that is, the angle must be 30º.



Intern
Joined: 03 Jan 2008
Posts: 7

Re: Each side of a certain parallelogram has length 6. If the area of the [#permalink]
Show Tags
28 Jan 2008, 09:40
2
This post received KUDOS
Given each side is 6 and area is 18. We can find the altitude, ie: alt = 18/6 = 3. Now we have a triangle with one side as 6, the alt as 3, and the base which we don't know.
Using Pythagoras theorem, 6^2 = 3^2 + Base^2 => Base = 3V3 So, the sides are now 3*1, 3*V3, 3*2 => 1:V3:2, which is a 306090 triangle.
Hence the angle that we know is 30, which forms a side of the parallelogram. Ans: A.



Director
Joined: 01 Jan 2008
Posts: 605

Re: Each side of a certain parallelogram has length 6. If the area of the [#permalink]
Show Tags
03 Mar 2008, 12:46
1
This post was BOOKMARKED
6*6*sin(alpha) = 18 > sin(alpha) = 1/2 > alpha = 30 > A



Intern
Joined: 20 Sep 2008
Posts: 46

Each side of a certain parallelogram has length 6. if the [#permalink]
Show Tags
25 Sep 2008, 14:26
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’
Equal sides of a parallegrame means it's a rhombus > angle should be either 60 or 120?



GMAT Tutor
Joined: 24 Jun 2008
Posts: 1346

Re: Parallelogram Angels [#permalink]
Show Tags
25 Sep 2008, 16:41
jugolo1 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’
Equal sides of a parallegrame means it's a rhombus > angle should be either 60 or 120? Well, you could rule out 60 and 120 right away, because if the parallelogram had an angle of 60 degrees, it would also need to have an angle of 120 degrees (adjacent angles in a parallelogram add to 180), and then there would be two correct answers to the question, which can't happen. The area of a parallelogram is base*height. The height of this parallelogram must be 3. We therefore need to find the angles in a right angled triangle with a hypotenuse of 6 and a height of 3. That's a 306090, of course, and 30 is the angle opposite the 3, so 30 degrees is one of the angle measures in the parallelogram, and 150 the other.
_________________
GMAT Tutor in Toronto
If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com



Intern
Joined: 25 Sep 2008
Posts: 1

Re: Parallelogram Angels [#permalink]
Show Tags
26 Sep 2008, 02:10
Ans is 30deg
area of a parallelogram = b*h
b*h=18 h=18/6=3
sin theta =opp/hyp= 3/6
theta = sin inv of 1/2=30 deg



Director
Joined: 23 May 2008
Posts: 762

Re: Parallelogram Angels [#permalink]
Show Tags
26 Sep 2008, 10:37
A=b*h or 1/2 d1*d2, if all 4 sides are equal then this is a rhombus, which is basically a tilted square. How can you have a height of 3 and area of 18? Shouldnt height be 6 and area 36? Is this question correctly worded?



GMAT Tutor
Joined: 24 Jun 2008
Posts: 1346

Re: Parallelogram Angels [#permalink]
Show Tags
26 Sep 2008, 10:52
bigtreezl wrote: A=b*h or 1/2 d1*d2, if all 4 sides are equal then this is a rhombus, which is basically a tilted square. How can you have a height of 3 and area of 18? Shouldnt height be 6 and area 36? Is this question correctly worded? If you have a rhombus with sides b and c, the area will only be b*c if the rhombus is a square. Otherwise the area will be less than b*c. To find the area of a rhombus (or any other parallelogram), you need to multiply the base and the height. If your parallelogram is 'tilted' (i.e. if the angles are not all 90 degrees), then the height is definitely not one of the sides. In this example, the rhombus is pretty seriously tilted to get an area as small as 18.
_________________
GMAT Tutor in Toronto
If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com



Director
Joined: 23 May 2008
Posts: 762

Re: Parallelogram Angels [#permalink]
Show Tags
26 Sep 2008, 11:18
1
This post received KUDOS



Manager
Status: IF YOU CAN DREAM IT, YOU CAN DO IT
Joined: 03 Jul 2017
Posts: 203
Location: India
Concentration: Finance, International Business

Re: Each side of a certain parallelogram has length 6. If the area of the [#permalink]
Show Tags
11 Aug 2017, 00:50
I have a question here. how are we considering the art of the parallelogram to be a right triangle?? Can someone please explain



PS Forum Moderator
Joined: 25 Feb 2013
Posts: 1003
Location: India
GPA: 3.82

Re: Each side of a certain parallelogram has length 6. If the area of the [#permalink]
Show Tags
12 Aug 2017, 12:47
longhaul123 wrote: I have a question here. how are we considering the art of the parallelogram to be a right triangle?? Can someone please explain HI longhaul123Can you be more specific with your query. If you drop a perpendicular on the base of the parallelogram then it will form a right angles triangle with one of the side of the parallelogram as its hypotenuse.



Director
Joined: 29 Jun 2017
Posts: 518
GPA: 4
WE: Engineering (Transportation)

Re: Each side of a certain parallelogram has length 6. If the area of the [#permalink]
Show Tags
10 Sep 2017, 07:30
Ans is clearly A see the attached image A= base x Height 6xH = 18 H=3 Sin A = 3/6 = 1/2 A=30 Answer is A
Attachments
IMG_0031.JPG [ 957.94 KiB  Viewed 1324 times ]
_________________
Give Kudos for correct answer and/or if you like the solution.



Manager
Status: Math Tutor
Joined: 12 Aug 2017
Posts: 74
WE: Education (Education)

Re: Each side of a certain parallelogram has length 6. If the area of the [#permalink]
Show Tags
11 Sep 2017, 00:53
We can work on options to get to the answer quickly, Option C and option E can be eliminated easily as if one angle is 60 one of the other angle has to be 120. Option D is not possible as if one angle is 90 all angles will be 90, thus it becomes a square with side 6 and area of square is 6*6 = 36. Not matching. Out of option A and option B, working on option A is easier, thus even if someone doesnt know how to work on this answer can still guess it correct. Now working on option A we can draw a diagonal and break parallelogram into two triangles of equal area. One angle of triangle is 30 and sides are 6. Using formula area of triangle = \(\frac{1}{2}\) * a*b*sin(x) area of one triangle becomes \(\frac{1}{2}\) * 6*6*sin(30) = \(\frac{1}{2}\) * 6*6*\(\frac{1}{2}\) = 9 Thus total area = 9+9 =18 Thus option A
_________________
Abhishek Parikh Math Tutor Whatsapp +919983944321 Mobile +971568653827 Website: http://www.holamaven.com




Re: Each side of a certain parallelogram has length 6. If the area of the
[#permalink]
11 Sep 2017, 00:53






