$\"\"$

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(a).

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The perimeter of rectangule is $\"\"$ .

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Consider length of rectangular is $\"\"$ and width of the rectangular is $\"\"$ ,Then perimeter of rectangular is $\"\"$ .

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

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if $\"\"$ then $\"\"$ .

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Substitute $\"\"$ in the equation $\"\"$ .

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$\"\"$

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$\"\"$ .

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The area of rectangle as a fucntion of width $\"\"$ is $\"\"$ .

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$\"\"$

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(b).

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Find the area of rectangle when width is maximum.

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$\"\"$ is the form of general quadratic equation

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Therefore $\"\"$ and $\"\"$ .

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The maximum area occurs at $\"\"$ .

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$\"\"$

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The maximum width is $\"\"$ .

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$\"\"$

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(c).

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Find the maximum area.

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Substitute $\"\"$ in the function $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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The maximum area is $\"\"$ .

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$\"\"$

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(a). $\"\"$

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(b).The maximum width is $\"\"$ .

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(c).The maximum area is $\"\"$ .