$\"\"$

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Observe the figure :

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The perimeter of the norman window is $\"\"$ is equals to $\"\"$ .

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$\"\"$

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Solve for $\"\"$ .

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$\"\"$

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Area of the Norman window :

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$\"\"$

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Consider $\"\"$ .

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

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$\"\"$

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$\"\"$

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$\"\"$ .

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

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$\"\"$

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For maximu area, $\"\"$ .

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$\"\"$

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$\"\"$

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If $\"\"$ , then

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$\"\"$

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$\"\"$ .

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$\"\"$

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The dimensions of norman window are $\"\"$ and $\"\"$ .