$\"\"$

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Find the length and width of the rectangle that has minimum perimeter.

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The area of the rectangle is $\"\"$ .

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Area of rectangle is $\"\"$ .

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$\"\"$

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

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

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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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Power rule of derivative : $\"\"$ .

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$\"\"$ .

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Equate derivative function to zero.

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$\"\"$ .

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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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Thus, the length and width of the rectangle are $\"\"$ and $\"\"$ .

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$\"\"$

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Length and width of the rectangle are $\"\"$ and $\"\"$ .