Question

If you use 128m of fencing, what is the largest possible rectangular area you can enclose? What is

Answer 1

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Answer:

• largest: 1024 m²
• smallest: 0 m²

Step-by-step explanation:

The largest rectangular area with a given perimeter is a square. Each side of the square will be 1/4 of the fence, or 32 m.

The largest enclosed area is (32 m)² = 1024 m².

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The smallest area will be that of an enclosure consisting of a double-row of fence: 64 m long and 0 m wide.

The smallest enclosed area is (64 m)(0 m) = 0 m².

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"Whole numbers" include zero. If you want the lengths to be Natural numbers, then the smallest area will be 63 m long and 1 m wide, or 63 m².