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

A rectangle is a special case of a parallelogram. One of the properties of this shape is that the intersection point of the diagonals divides each of them in half. We also need the fact that the opposite sides of a parallelogram are equal by definition. And only the rectangle has equal diagonals. Therefore, triangle AOD has AO = OD = BD / 2. Thus, the perimeter is 15/2 + 15/2 + 12 = 27.