Area of a triangle: A (triangle )= 4 · 6 / 2 = 12 ft² 150 - 12 = 138 ft² ( the maximum area of the rectangle ) L = ? W = 6 ft A ( rectangle ) = L · W L · 6 = 138 L = 138 : 6 = 23 ft. Answer: the maximum length of the base of the rectangle he can build is 23 ft.