Prime Square

Geometry Level 2

A red rectangle is reshaped into a blue square, as shown below, such that both quadrilaterals have the same perimeter. The area of the square is 4 cm24\text{ cm}^2 larger than that of the rectangle.

If all the sides of both quadrilaterals have prime number lengths ((in cm),\text{cm}), then what is the perimeter of the square?

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