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geometry

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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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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by 2010gmat » Sun Nov 29, 2009 1:44 am
how about a circle?? or say a triangle
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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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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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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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