$\"\"$

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Let $\"\"$ be the length of the rectangle and $\"\"$ be the width of the rectangle.

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Area of the rectangle $\"\"$ .

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Find $\"\"$ in terms of $\"\"$ .

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Perimeter of the rectangle $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$ .

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$\"\"$

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$\"\"$ .

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Differentiate on each side with respect to $\"\"$ .

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$\"\"$

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Find the critical numbers by equating derivative to zero.

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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Since the second derivative of $\"\"$ is negative, it gives a maximum.

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$\"\"$ is maximum when $\"\"$ and $\"\"$ .

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There are no dimensions that yield a minimum area.

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Explanation :

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This can be made by arbitrary small by selecting $\"\"$ .

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$\"\"$

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$\"\"$ is maximum when $\"\"$ and $\"\"$ .

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There are no dimensions that yield a minimum area.

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Explanation :

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This can be made by arbitrary small by selecting $\"\"$ .