The parallelogram bounded by the lines y = ax + c, y = ax + d, y = bx + c, and y = bx + d has area 18. The parallelogram bounded by the lines y = ax + c, y = ax - d, y = bx + c, and y = bx - d has area 72. Given that a, b, c, and d are positive integers, what is the smallest possible value of a + b + c + d ?
Interactive version of problem and solution.
