Find all School-related info fast with the new School-Specific MBA Forum

It is currently 23 Oct 2014, 07:48

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Help with Quant question

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
Intern
Intern
avatar
Joined: 08 Dec 2012
Posts: 2
Followers: 0

Kudos [?]: 0 [0], given: 1

Help with Quant question [#permalink] New post 23 Dec 2012, 08:02
Hi,
Im working on an easy quant question but this book does not explain much, so I need your help!

The question is:

Parallelogram ABCD has an area of 52 sq centimeters, a height of 4 centimeters and an angle with measure 60 degrees. What is the perimeter of parallelogram ABCD?

my answer was 32 but the book has 26+(16 root 3/3)

since the area is 52, i got that the sides were 13, and 4 (given)... so the total perimeter is (13*2) + (4*2)

How did they get 16 root 3 / 3? ?
Expert Post
Magoosh GMAT Instructor
User avatar
Joined: 28 Dec 2011
Posts: 2142
Followers: 539

Kudos [?]: 2273 [0], given: 31

Re: Help with Quant question [#permalink] New post 23 Dec 2012, 19:49
Expert's post
onedergyal wrote:
Hi,
Im working on an easy quant question but this book does not explain much, so I need your help! The question is:
Parallelogram ABCD has an area of 52 sq centimeters, a height of 4 centimeters and an angle with measure 60 degrees. What is the perimeter of parallelogram ABCD?

my answer was 32 but the book has 26+(16 root 3/3)

since the area is 52, i got that the sides were 13, and 4 (given)... so the total perimeter is (13*2) + (4*2)

How did they get 16 root 3 / 3? ?

I'm happy to help with this. :-)
Attachment:
parallelogram, area = 52.JPG
parallelogram, area = 52.JPG [ 24.19 KiB | Viewed 400 times ]

First of all, it sounds like you were treating the situation as if it were a rectangle, not a parallelogram. If 4 is the height, then 4 would NOT be the "slant length" of the sides. In the diagram, BE = 4 but AB and CD do not equal 4. This is a very common mistake folks make about parallelograms. The "height" is not the length of the slant.

You correctly figured out, from the area, that AD = BC = 13.

To find the length of AB = CD, we have to use the properties of the 30-60-90 triangle. Here's a blog to refresh your memory on these:
http://magoosh.com/gmat/2012/the-gmats- ... triangles/

Triangle ABE is a 30-60-90 triangle. For the 30-60-90 triangle, we can remember
hypotenuse:2
short leg:1
long leg: sqrt(3)

We know the long leg, BE = 4 and we want the hypotenuse.

long leg/hypotenuse = sqrt(3)/2
4/(AB) = sqrt(3)/2
8 = (AB)*sqrt(3)
AB = 8/sqrt(3)
Now, because we have a radical in the denominator, we are going to use a procedure you may recall from algebra two: rationalizing the denominator. We will multiply both the numerator and the denominator by sqrt(3). This has the effect of removing the radical from the denominator.
AB = [8/sqrt(3)]*[sqrt(3)/sqrt(3)] = [8*sqrt(3)]/3

perimeter = 2*(AD) + 2*(AB) = 26 + [16*sqrt(3)]/3
Voila! The OA.

Does all this make sense?
Mike :-)
_________________

Mike McGarry
Magoosh Test Prep

Image

Image

Intern
Intern
avatar
Joined: 08 Dec 2012
Posts: 2
Followers: 0

Kudos [?]: 0 [0], given: 1

Re: Help with Quant question [#permalink] New post 27 Dec 2012, 11:10
thanks for the reply! i just noticed that there was a response... Here is where I'm lost
I get that in a 30/60/90 triangle that the angle across from 60 is (x root 3)... so since that value is 4, I set 4 = to x root 3, then solve for x... so the length of that side is (4/root3.. and since root3 is in the demonimator.. its 4root3?) , so X =4, and 2x =8?
Expert Post
Magoosh GMAT Instructor
User avatar
Joined: 28 Dec 2011
Posts: 2142
Followers: 539

Kudos [?]: 2273 [0], given: 31

Re: Help with Quant question [#permalink] New post 27 Dec 2012, 21:00
Expert's post
onedergyal wrote:
thanks for the reply! i just noticed that there was a response... Here is where I'm lost
I get that in a 30/60/90 triangle that the angle across from 60 is (x root 3)... so since that value is 4, I set 4 = to x root 3, then solve for x... so the length of that side is (4/root3.. and since root3 is in the demonimator.. its 4root3? NO!) , so X =4, and 2x =8? NO!

When you divide by a root, you need to rationalize the denominator. This means you have to multiply both the numerator and the denominator by that root, so that the product in the denominator produces an integer. Rationalizing the denominator is a very important procedure to understand for GMAT math. It is absolutely 100% false that 4/sqrt(3) is the same as, or anything even vaguely related to, 4*sqrt(3). Furthermore, the sqrt(3)'s do not simply cancel and disappear. Rather
Attachment:
four over root three.JPG
four over root three.JPG [ 11.92 KiB | Viewed 361 times ]

That cannot be simplified any further. That expression on the right is the absolutely simplest mathematical form in which we can write this value. Since this is what x is, 2x would be twice this ------ 8*sqrt(3)/3
Does this make sense?
Mike :-)
_________________

Mike McGarry
Magoosh Test Prep

Image

Image

Re: Help with Quant question   [#permalink] 27 Dec 2012, 21:00
    Similar topics Author Replies Last post
Similar
Topics:
Need help with quant questions. mahadfarrukh 0 06 Nov 2012, 08:09
Quant Coursework Question - Please help!!! MoonlightGrahm 1 18 Jul 2012, 06:36
6 Help with Quant questions Patcheko80 10 31 Oct 2011, 03:54
Quant Questions-please help me solve these nitinneha 8 18 Mar 2007, 18:04
GMAT Prep Quant Questions - Please Help zippo 1 28 Oct 2006, 10:06
Display posts from previous: Sort by

Help with Quant question

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.