I'm pretty sure the diagram you drew of the box's position is correct. First, put the origin at the base of the arch, not at the vertex. This makes the equation y = 58-58/196*x^2. Label one corner of the box at its upper right. Call this point (x,y). We know that y = 2x from the shape of the box (the height is twice half of the bottom side length), and y = 58-58/196*x^2 from the arch (the corner touches the arch). Combine these equations to get 58/196*x^2+2x-58 = 0. Solve for x, which I trust you know how to do at this point. The positive solution, x = 14/29*(âˆš890 - 7), is half the side length of the box.