The parallelogram ABCD has a diagonal BD = 2. The angles of the triangle BCD are equal or they are equal to 60 degrees. As the diagonal intersects the parallelogram into two congruent triangles we have the angle A = angle C = 60 degrees and the angle B = angle D = 120 degrees.
As the triangle BCD has equal angles, so are its sides. This gives BC = CD = BD = 2
The perimeter of the parallelogram is 2 + 2 + 2 + 2 = 8
The perimeter of ABCD is 8 units.
Since all the angles of triangle BCD are equal, that means that the triangle BCD is equilateral, therefore BD = BC = CD = 2.
Since ABCD is parallelogram, then BC=AD = 2 and AB = CD = 2.
The perimeter of the parallelogram ABCD is:
P = AB+BC+CD+AD
P = 4*AB
P = 4*2
P = 8 units
The requested perimeter of the parallelogram ABCD is of 8 units.