This answer can be derived using proportionality. To maximize height, figure out the farthest that the barge can be from the angle created on the left side. Since the barge is 30 meters wide, the farthest it can be from the left side is 26 meters. The bridge forms a right triangle. Draw the height connecting the bridge and a point 30 meters into the river from the tallest side.
Height is perpendicular because it is the shortest distance from a point to a line.
Height of the abuttment and the height drawn connecting the river to the bridge are parallel because both are perpendicular to the same line. Forms two similar triangles because if a parallel line is drawn to any side of a triangle, it forms two similar triangles. Therefore, a barge 30 m wide and 6.6 m or less high will fit under the bridge. If the company's biggest barges were 30 meters in length, they have to have a height requirement because of the bridge. The river itself was 46 meters in length.