Question

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

Answer 1

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:
$$\begin{gathered} OB=\frac{1}{2}\left(8\right)\mathrm{cm} \\ OB=4\mathrm{cm} \\ \mathrm{and}OD=\frac{1}{2}\left(8\right)\mathrm{cm} \\ OD=4\mathrm{cm} \end{gathered}$$
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.