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Malika's rectangular garden is enclosed with 24 m of fencing.
What is the least possible area of Malika's garden?
What is the greatest possible area?

Sagot :

AL2006idn
The greatest possible area with a fixed length of fencing (perimeter) is a circle.

Circumference = 2 pi x radius = 24 m
Radius = (24 m) / (2 pi) = 12 m / pi

Area of a circle = pi x radius squared = (pi) x (12 m / pi)^2 = 144 / pi = 45.837 square meters.
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The rectangle with the greatest possible area for a fixed perimeter is the square.

Each side of the square = 24 / 4 = 6 meters

Area of a square = (side) squared = 36 square meters 
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There is no 'least possible' area.  The longer and skinnier you make it,
the less area it will have.

Here are some examples. Each one has 24 m of fencing:

5 m x 7 m = 35 square meters
4 x 8 = 32 square meters
3 x 9 = 27 square meters
2 x 10 = 20 square meters
1 x 11 = 11 square meters
0.5 x 11.5 = 5.75 square meters
0.1 x 11.9 = 1.19 square meters
1 centimeter x 11.99 meters = 0.1199 square meters
1 millimeter by 11.999 meters = 0.011999 square meters

The longer and skinnier the garden is, the less area it has.

 








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