Construct the diagram and you will find two right angled triangles. The hypotenuse of this triangle is the side of the parallelogram, and the altitude is the side of the rectangle. It's a given fact that the hypotenuse is always greater than the altitude, so therefore sum of two sides of the parallelogram are greater than sum of two sides of the rectangle. The other two sides of the rectangle and parallelogram are equal, so they're sums are the same.
Hence, because of two larger sides, parallelogram has greater perimeter than rectangle.