Construct a square, each of whose diagonals measures 5.8 cm.

We know that the diagonals of a square bisect each other at right angles.

Steps of construction:

Step 1: Draw $A C=5.8 \mathrm{~cm}$

Step 2: Draw the perpendicular bisector $X Y$ of $A C$, meeting it at $O$.

Step 3:From $O$ :

$O B=\frac{1}{2}(5.8) \mathrm{cm}=2.9 \mathrm{~cm}$

$O D=\frac{1}{2}(5.8) \mathrm{cm}=2.9 \mathrm{~cm}$

Step 4: Join AB, BC, CD and DA.

ABCD is the required square.