Geometry Square and Parellelogram

Expert replies

kop: Junior | Next Rank: 30 Posts; Posts: 29; Joined: Thu Oct 03, 2013 11:35 am; Thanked: 1 times

by kop » Wed Nov 20, 2013 12:06 am

A square ABCD is drawn and point E is marked on AB such that AE=AB/3. Similarly points F, G and H are marked on the sides of the square such that BF=BC/3, CG=CD/3 and DH=DA/3. If the points E, F, G, and H are connected to make a parallelogram, what is the ratio of the area of square ABCD to the area of parallelogram EFGH?

81/16
9/4
9/5
5/4
4/5

Last edited by kop on Wed Nov 20, 2013 3:08 am, edited 1 time in total.

Like this post

Source: Beat The GMAT — Problem Solving | Wed Nov 20, 2013 12:06 am

theCodeToGMAT: Legendary Member; Posts: 1556; Joined: Tue Aug 14, 2012 11:18 pmFollowed by: 34 members; Thanked: 448 times; GMAT Score:650

by theCodeToGMAT » Wed Nov 20, 2013 12:40 am

kop wrote:A square ABCD is drawn and point E is marked on AB such that AE=AB3. Similarly points F, G and H are marked on the sides of the square such that BF=BC3, CG=CD3 and DH=DA3. If the points E, F, G, and H are connected to make a parallelogram, what is the ratio of the area of square ABCD to the area of parallelogram EFGH?

81/16
9/4
9/5
5/4
4/5

Is the question transcribed correctly?

R A H U L

Like this post

kop: Junior | Next Rank: 30 Posts; Posts: 29; Joined: Thu Oct 03, 2013 11:35 am; Thanked: 1 times

by kop » Wed Nov 20, 2013 3:09 am

sorry !! edited now

Like this post

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Wed Nov 20, 2013 4:06 am

kop wrote:A square ABCD is drawn and point E is marked on AB such that AE=AB/3. Similarly points F, G and H are marked on the sides of the square such that BF=BC/3, CG=CD/3 and DH=DA/3. If the points E, F, G, and H are connected to make a parallelogram, what is the ratio of the area of square ABCD to the area of parallelogram EFGH?

81/16
9/4
9/5
5/4
4/5

PLUG IN an easy figure that satisfies all of the given constraints:

Square ABCD:
Area = sÂ² = 3Â² = 9.

âˆ†AEH, âˆ†BEF, âˆ†CFG, and âˆ†DGH:
Area of each triangle = (1/2)bh = (1/2)*2*1 = 1.
Combined area of the 4 triangles = 4*1 = 4.

EFGH:
Area = (square ABCD) - (combined area of the 4 triangles) = 9-4 = 5.

Resulting ratio:
ABCD/EFGH = 9/5.

The correct answer is C.

Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

Like this post

Mathsbuddy: Master | Next Rank: 500 Posts; Posts: 447; Joined: Fri Nov 08, 2013 7:25 amFollowed by: 1 member; Thanked: 25 times

by Mathsbuddy » Thu Nov 21, 2013 10:01 am

ABCD area = 3^2 = 9

Each triangle has area (1 * 2)/2 = 1
4 triangles area = 1 * 4 = 4

9-4 = 5

Answer = 9/5

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

559 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review