geometry

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2010gmat: Master | Next Rank: 500 Posts; Posts: 371; Joined: Fri Mar 06, 2009 2:48 am; Thanked: 27 times; GMAT Score:740

by 2010gmat » Sun Nov 29, 2009 12:03 am

Say we have a arope of length 28 mts.

What is the maximum area that can be enclosed using this rope and what is the minimum area that can be enclosed?

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Source: Beat The GMAT — Problem Solving | Sun Nov 29, 2009 12:03 am

sunnyjohn: Master | Next Rank: 500 Posts; Posts: 344; Joined: Mon Sep 14, 2009 5:40 amFollowed by: 3 members; Thanked: 28 times; GMAT Score:700

by sunnyjohn » Sun Nov 29, 2009 1:09 am

I think... Square will give u maximum area and rectangle will minimum area

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2010gmat: Master | Next Rank: 500 Posts; Posts: 371; Joined: Fri Mar 06, 2009 2:48 am; Thanked: 27 times; GMAT Score:740

by 2010gmat » Sun Nov 29, 2009 1:44 am

how about a circle?? or say a triangle

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horlhaf: Newbie | Next Rank: 10 Posts; Posts: 1; Joined: Sun Nov 22, 2009 8:20 am

by horlhaf » Sun Nov 29, 2009 7:29 am

The way I see it is:

Biggest is a circle

28 / pi = c. 9 (circumference) --> Area therefore c. 62

Second is an equilateral triangle - other shapes of triangles should be smaller

28 / 3 = 9 1/3 --> Area c. 60.5

Third is square

28 / 4 = 7 --> Area is 49

Rectangle is smallest

Range from (using integers) 1x13 = 13 to 6x8 = 48

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2010gmat: Master | Next Rank: 500 Posts; Posts: 371; Joined: Fri Mar 06, 2009 2:48 am; Thanked: 27 times; GMAT Score:740

by 2010gmat » Sun Nov 29, 2009 8:49 am

u re right,..circle will have the max area...

but am not sure about the figure with smallest area...stuck between rectangle and triangle...

u re also right that equilateral triangle will have max area...and thats a rule in general...among quadrilaterals square will have max area...

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sun Nov 29, 2009 9:49 am

2010gmat wrote:u re right,..circle will have the max area...

but am not sure about the figure with smallest area...stuck between rectangle and triangle...

u re also right that equilateral triangle will have max area...and thats a rule in general...among quadrilaterals square will have max area...

We can construct both rectangles AND triangles such that their areas approach 0.
For a rectangle, just let the width get very very very close to zero, and the area will approach zero.
For a triangle, just let the height get very very very close to zero, and the area will approach zero.

Brent Hanneson - Creator of GMATPrepNow.com

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