The diagonals of rectangle ABCD meet at point O. Find the perimeter of triangle AOD if AB = 9, BC = 12, BD = 15.

By condition, we are given a rectangle, then using the properties of the rectangle, namely, that the diagonals of the rectangle are equal and when they intersect are divided in half, we can immediately say that the lengths of AO and OD are equal:
AO = OD = (1/2) * BD = (1/2) * 15 = 7.5 cm.
The length of the BC is equal to the length of AD and is equal to 12 cm, then the perimeter of the triangle AOD is equal to:
P = AO + OD + AD = 7.5 + 7.5 + 12 = 27 cm.
Answer: The perimeter of triangle AOD is 27 cm.