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

It is currently 29 Aug 2014, 08:11

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

greatest area of a rectangle inscribed in a circle

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Manager
Manager
avatar
Joined: 05 Oct 2005
Posts: 201
Followers: 1

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

GMAT Tests User
greatest area of a rectangle inscribed in a circle [#permalink] New post 02 Jun 2006, 09:51
hello
does anyone have the mathematically correct way to compute the greatest area of a rectangle inscribed in a circle given its diameter D

thanks :)
_________________

when there is a will there is a way

best regards

Director
Director
User avatar
Joined: 04 Jan 2006
Posts: 928
Followers: 1

Kudos [?]: 12 [0], given: 0

GMAT Tests User
 [#permalink] New post 02 Jun 2006, 19:27
this is interesting.. i would like to be in the loop if someone does get the answer!
2 KUDOS received
VP
VP
User avatar
Joined: 29 Dec 2005
Posts: 1351
Followers: 6

Kudos [?]: 28 [2] , given: 0

GMAT Tests User
Re: greatest area of a rectangle inscribed in a circle [#permalink] New post 02 Jun 2006, 20:05
2
This post received
KUDOS
mand-y wrote:
hello
does anyone have the mathematically correct way to compute the greatest area of a rectangle inscribed in a circle given its diameter D
thanks :)


i like the question.

square is the greatest ractangal that can be inscribed in the circle with diameter D.
S = side of the square
S^2+S^2 = D^2
S = D/sqrt(2)

A (area of the square) = D^2/2

if D = 10, A = 50.
VP
VP
avatar
Joined: 21 Sep 2003
Posts: 1071
Location: USA
Followers: 3

Kudos [?]: 30 [0], given: 0

GMAT Tests User
 [#permalink] New post 02 Jun 2006, 20:18
Prof is right. I don't think we need to know how to prove this, but it requires differentiation..

Area = l*w

d^2 = l^2+w^2
=>w = SQRT(d^2-l^2)

Hence A = l*(d^2-l^2)^1/2

To find the maxima of this fn, we ned to differentiate this eqn and set
dA/dl = 0
=> 2*l^2 = d^2
=> l = d/SQRT(2) & w = d/SQRT(2)
_________________

"To dream anything that you want to dream, that is the beauty of the human mind. To do anything that you want to do, that is the strength of the human will. To trust yourself, to test your limits, that is the courage to succeed."

- Bernard Edmonds

  [#permalink] 02 Jun 2006, 20:18
    Similar topics Author Replies Last post
Similar
Topics:
2 Experts publish their posts in the topic Rectangle ABCD is inscribed in circle P. What is the area of AccipiterQ 2 21 Oct 2013, 07:36
2 Experts publish their posts in the topic Area of a rectangle inscribed in a circle of radius r iwantto 4 16 Apr 2013, 15:49
59 Experts publish their posts in the topic A rectangle is inscribed in a circle of radius r. If the alex1233 31 16 May 2012, 06:44
3 Experts publish their posts in the topic The area of a rectangle inscribed in a circle is 12. Area of smitakokne 5 19 Dec 2010, 06:29
1 Experts publish their posts in the topic The interior of a circle is inscribed in a rectangle of side bmwhype2 14 03 Mar 2008, 13:27
Display posts from previous: Sort by

greatest area of a rectangle inscribed in a circle

  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®.