AB = 5.8 cm, diagonal AC = 8.2 cm and diagonal BD = 6.2 cm.

Steps of construction :

1. Draw a line segment AB = 5.8 cm

2. Since diagonals of a parallelogram bisect each other; construct triangle OBC, such that :

OB = $\dfrac{1}{2}BD = \dfrac{1}{2} \times 6.2$ = 3.1 cm

OA = $\dfrac{1}{2}AC = \dfrac{1}{2} \times 8.2$ = 4.1 cm

3. Produce BO upto D, such that OD = OB = 3.1 cm and produce AO upto C, such that OC = OA = 4.1 cm.

4. Join BC, CD and AD.

Hence, ABCD is the required parallelogram.