If 𝐴𝐵𝐶𝐷  is a rectangle, 'O'  is the intersection point of diagonals and 𝑂𝐴 = 9cm , then 𝐵𝐷 =

𝑂𝐴 = 9cm

In rectangle diagonals are equal.

i.e.,$AC=BD$

diagonals bisect each other

$AO=OC,OB=OD$(midpoint of diagonals are equal)

Given $OA=9$

$2\times OA=BD$

$2\times 9=BD$

$BD=18\mathrm{cm}$