$\"\"$

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The perimeter of the rectangle is $\"\"$ units.

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Find the length and width of the rectangular that has the maximum area.

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Formula for the perimeter of the rectangle is $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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Formula for the rectangle area is $\"\"$ .

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

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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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$\"\"$ .

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

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$\"\"$

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$\"\"$

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

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Length and width of the rectangle is $\"\"$ units, $\"\"$ units.

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$\"\"$

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Length and width of the rectangle is $\"\"$ units, $\"\"$ units.