The correct option is A 5 cm
ABCD is a rhombus.
Perimeter of the rhombus is 80 cm.
If, length of one side of the rhombus is a, then,
⇒ a+ a+ a+ a = 80
⇒ 4a = 80
⇒ a =804 = 20
Length of a side of rhombus = 20 cm.
Then, AB = 20 cm.
BD = 12 AB
BD = 12 × 20 = 10
BD = 10 cm.
Since, BD is the diagonal, and the diagonals of a rhombus are perpendicular bisectors, BO = OD
⇒ BD = BO +OD = BO + BO
⇒ BD = 2 BO
⇒ 10 = 2 BO
⇒ BO =102 = 5 cm.
The length of BO is 5 cm.