An open box is to be made out of a 12-inch by 16-inch piece of cardboard by cutting out squares of equal size from the four corners and bending up the sides. find the dimensions of the resulting box that has the largest volume.

Each square of the box made from a piece of cardboard must be 4-inches by 4-inches given the starting dimensions of a 12-inch by 16-inch rectangle. A box can be made by using a rectangle by folding a t-shape. The ratio of the length and width confines our t-shape to be 3 squares wide by 4 squares tall which is perfect for a cube. Divide the dimensions by the respective sides square and you will find the answer.