circles in a rectangle - difficult problem! - The Beat The GMAT Forum

circles in a rectangle - difficult problem!

Expert replies

bhumika.k.shah: Legendary Member; Posts: 941; Joined: Sun Dec 27, 2009 12:28 amFollowed by: 1 member; Thanked: 20 times

by bhumika.k.shah » Sat Jan 30, 2010 12:06 am

The two circles shown in the diagram touch rectangle ABCD at exactly three points each, and touch each other at exactly one point. If the diagonal of rectangle ABCD is sq rt 80 centimeters long, what is the area of one of the circles, in square centimeters?

A 4pie
B 8 pie
C 16 pie
D 25 pie
E 64 pie

Attachments

Last edited by bhumika.k.shah on Sat Jan 30, 2010 12:24 am, edited 1 time in total.

Like this post

Source: Beat The GMAT — Problem Solving | Sat Jan 30, 2010 12:06 am

thephoenix: Legendary Member; Posts: 1560; Joined: Tue Nov 17, 2009 2:38 amFollowed by: 5 members; Thanked: 137 times

by thephoenix » Sat Jan 30, 2010 12:20 am

pls mention the length of diag

Like this post

bhumika.k.shah: Legendary Member; Posts: 941; Joined: Sun Dec 27, 2009 12:28 amFollowed by: 1 member; Thanked: 20 times

by bhumika.k.shah » Sat Jan 30, 2010 12:29 am

Done!

thephoenix wrote:pls mention the length of diag

Like this post

thephoenix: Legendary Member; Posts: 1560; Joined: Tue Nov 17, 2009 2:38 amFollowed by: 5 members; Thanked: 137 times

by thephoenix » Sat Jan 30, 2010 12:32 am

bhumika.k.shah wrote:The two circles shown in the diagram touch rectangle ABCD at exactly three points each, and touch each other at exactly one point. If the diagonal of rectangle ABCD is sq rt 80 centimeters long, what is the area of one of the circles, in square centimeters?

A 4pie
B 8 pie
C 16 pie
D 25 pie
E 64 pie

IMO A
pls mention the length of diag

let width of rect be x ; then length=2x

d=diag

d^2=x^2+(2x)^2
=5x^2

x=d/ ryt5=d(rut 5)/5

x/2=d(rut5)/10

area of circle=pie(x/2)^2
=pie* (d^2)5/100=d^2/20=(rut80)^2/20=4pie

Like this post

sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Sat Jan 30, 2010 3:16 am

bhumika.k.shah wrote:The two circles shown in the diagram touch rectangle ABCD at exactly three points each, and touch each other at exactly one point. If the diagonal of rectangle ABCD is sq rt 80 centimeters long, what is the area of one of the circles, in square centimeters?

A 4pie
B 8 pie
C 16 pie
D 25 pie
E 64 pie

The rectangle has its length twice of its width in here. So, if x cm is width, 2 x cm is the length; such that:

x^2 + (2 x) ^2 = 80

Or x = 4, same as the diameter of each circle in here; the area of each of the circles in here is therefore, [spoiler]4 Ï€[/spoiler] square centimeter.

[spoiler]A[/spoiler]

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 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