$\"\"$

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The perimeter of rectangular 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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But one side width has covered by a river,hence the perimeter need to be fenced 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 is $\"\"$ .

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$\"\"$

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Find the maximum area of rectangle.

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The maximum area of rectangle occurs when the length is maximum.

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

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

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

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$\"\"$

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The maximum length is $\"\"$ .

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Substitute $\"\"$ in the function $\"\"$ to get the maximum area.

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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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The maximum area is $\"\"$ .