My confusion is this: since the figures are not drawn to scale, shouldn’t the rectangle inside the square be able to take many possible shapes and positions? In that case, couldn’t the shaded rectangle have a perimeter that is equal to the square’s perimeter or smaller than it, depending on how it is positioned? If so, why wouldn’t the correct answer be D, instead of A?
Try drawing it in different positions for which you can solve its sides if this isn’t intuitive for you.