$\"\"$

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Observe the rectangle:

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Find width of the shaded rectangle.

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Let $\"\"$ be a side of the smaller square of area $\"\"$ .

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Since, $\"\"$ .

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$\"\"$ (Take square root of each side)

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$\"\"$ (Cancel square and root)

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$\"\"$ (Substitute: $\"\"$ )

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Therefore, the width of the shaded rectangle is $\"\"$ .

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Find length of the shaded rectangle.

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Let $\"\"$ be a side of the smaller square of area $\"\"$ .

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Since, $\"\"$ .

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$\"\"$ (Take square root of each side)

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$\"\"$ (Cancel square and root)

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$\"\"$ (Substitute: $\"\"$ )

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Therefore, the length of the shaded rectangle is $\"\"$ .

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$\"\"$

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Find the perimeter of the two rectangles.

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Perimeter of the rectangle is $\"\"$ .

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The sum of the perimeters of the two shaded rectangles is $\"\"$ .

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$\"\"$ (Add: $\"\"$ )

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$\"\"$ (Multiply)

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$\"\"$ (Add: $\"\"$ )

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Therefore,The sum of the perimeter of the rectangles are $\"\"$ .

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$\"\"$

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Option D is right choice.