Given data: Length or wire needed to fence both the rectangle and the square is the same.

The side of the square is twice the width of the rectangle.

Area(Square) - Area(Rectangle) = 100

We have been asked to find the area of the square

Let the length and width of the rectangle be y and x.

From the question stem, side of square is 2x

\(2(y+x) = 4(2x)\)

Therefore, \(y = 4x-x =3x\)

We know that Area(Square) - Area(Rectangle) = 100

Therefore \(4x^2 - x(3x) = 100 => x^2 = 100 => x = 10\)(because side cannot be negative)

Hence, area of square is \((2x)^2 = 20^2 = 400\)

(Option C)
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