You can start be calling angle ADC = theta; then since |DA| = x you have |AC| = x sin(theta), and angle BAC = theta. Draw a line from C to be perpendicular to AB - this is the height of triangle ABC, which is |AC|sin (theta) = x sin^2(theta). Given the area of triangle ABC = 24, we get 24 = (1/2)x^2sin^2(theta). To minimize x you want to maximize sin^2(theta). Take it away...