Construct a rhombus the lengths of whose diagonals are 6 cm and 8 cm.

We know that the diagonals of a rhombus bisect each other.

Steps of construction:

Step 1: Draw AC= 6cm

Step 2:Draw a perpendicular bisector(XY) of AC, which bisects AC at O.

Step 3: $O B=\frac{1}{2}(8) \mathrm{cm}$

$O B=4 \mathrm{~cm}$

and $O D=\frac{1}{2}(8) \mathrm{cm}$

$O D=4 \mathrm{~cm}$

Draw an arc of length 4 cm on OX and name that point as B.

Draw an arc of length 4 cm on OY and name that point as D.

Step 4 : Join AB, BC, CD and AD.​

Thus, ABCD is the required rhombus, as shown in the figure.