$\"\"$

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The perimeter inside playing area is $\"\"$ .

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Consider the width is $\"\"$ and the length is $\"\"$ .

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

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The rectangle have two semicircles on each side, i.e $\"\"$ .

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$\"\"$

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The area of play ground is $\"\"$ .

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Substitue $\"\"$ in the above equation

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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The equation is $\"\"$ .

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The area is maximum when the heigt is at $\"\"$ .

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$\"\"$ ,here $\"\"$ and $\"\"$ .

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Substitue above values into $\"\"$ .

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$\"\"$

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$\"\"$

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The area is maximum when length is $\"\"$ .

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Substitue $\"\"$ in $\"\"$ .

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$\"\"$

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The area is maximum when width is $\"\"$ .

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$\"\"$

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The area is maximum when length is $\"\"$ and width is $\"\"$ .