James had a rectangular piece of cardboard that was four times as long as it was wide. He wanted to use the cardboard to make a box with no lid. To do this, he first cut a 4-by-4 inch square out of each of the four corners of the piece of cardboard, as shown in the picture below. Then James folded the cardboard along the four dotted lines shown in the picture. This created an open box with a volume of 432 cubic inches. What was the width of the sheet of cardboard that james started with?

Question

James had a rectangular piece of cardboard that was four times as long as it was wide. He wanted to use the cardboard to make a box with no lid. To do this, he first cut a 4-by-4 inch square out of each of the four corners of the piece of cardboard, as shown in the picture below.  Then James folded the cardboard along the four dotted lines shown in the picture. This created an open box with a volume of 432 cubic inches. What was the width of the sheet of cardboard that james started with?