One diagonal = 5.4 cm.

Steps of construction :

1. Draw AC = 5.4 cm.

2. Draw XY, the perpendicular bisector of AC, meeting AC at O.

3. With O as center and radius equal to $\dfrac{5.4}{2}$ = 2.7 cm, draw an arc cutting XY at B and D.

4. Join AB, BC, CD, and DA.

Hence, ABCD is the required square.