Malika's rectangular garden is enclosed with 24 m of fencing.

1. What is the least possible area of Malika's garden?
2. What is the greatest possible area of Malika's garden?

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.
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 **
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.

Answered by AL2006 | 2024-06-10

The least possible area of Malika's garden approaches 0 square meters if the garden becomes very thin. The greatest possible area occurs when the garden is a square, which is 36 square meters.
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Answered by AL2006 | 2024-12-21