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

Given:
rectangle ABCD,
AC and BD diagonals,
point O of intersection of the diagonals AC and BD,
AB = 9,
BC = 12,
BD = 15.
Find the perimeter of a triangle AOD -?
Decision:
Consider the triangle AOD. Its sides AO = OD = 15: 2 = 7.5 since the diagonals in the rectangle are equal to each other and the intersection point is divided in half.
We know that the opposite sides of the rectangle are equal, then BC = AD = 12.
Then the perimeter of the triangle ABD will be equal to:
P = AO + OD + AD;
P = 7.5 + 7.5 + 12;
P = 15 + 12;
P = 27.
Answer: The perimeter of triangle AOD is 27.