Construction of a square when the diagonal is known
Let us construct a square with one of its diagonals as \(10\) \(cm\).
Step \(1\): Draw a rough diagram with the measurements known.
Step \(2\): Draw a line segment \(AC\) of length \(10\) \(cm\).
Step \(3\): Draw a perpendicular bisector to \(AC\) such that the bisector intersects \(AC\) at \(O\).
Step \(4\): With \(O\) as centre and with \(5\) \(cm\) as radius, draw arcs on both sides of the perpendicular bisector. Mark the intersections as \(B\) and \(D\).
Step \(5\): Join \(AB\), \(BC\), \(CD\), and \(AD\) to form the desired square.
Thus, \(ABCD\) is the required square.