Question
Construct a square in which each diagonal is $5\ cm$ long.
✓
Answer
Steps of Construction:
$1.$ Draw $\text{AC} = 5\ cm$
$2.$ With $A$ as centre, draw arc length slightly greater than $\frac{1}{2}$ $\text{AC}$ above $\&$ below the line segment $\text{AC}$.
$3.$ With $C$ as centre, draw an arc of same length as in step $2$ above $\&$ below the line segment $\text{AC}$ which intersect the arcs drawn in Step $2$.
$4.$ Join both the intersection points obtained in step $3$ by a line segment which intersects $\text{AC}$ at $O$.
$5.$ With $O$ as centre cut off $\text{OB = OD} = 2.5\ cm$ along the bisector line.
$6.$ Join $\text{AD, CD, AB}$ and $\text{CB}$.
Hence, this is the required square.
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