MHB Dimension of the cut-out squares that result in largest possible side area

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The discussion centers on maximizing the side area of a topless square box created by cutting squares from the corners of a 12-inch metal sheet. The variable "x" represents the side length of the cut-out squares, leading to a box length of 12-2x once folded. The total side area is expressed as A = 4x(12-2x), focusing on the area of all four sides. There is some confusion regarding the interpretation of "largest side area," whether it refers to the area of one side or all four sides, but calculations yield consistent results regardless of interpretation. Ultimately, the goal is to determine the optimal dimensions of the cut-out squares for maximum side area.
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A topless square box is made by cutting little squares out of the four corners of a square sheet of metal 12 inches on a side, and then folding up the resulting flaps. What is the largest side area which can be made in this way?

What information I have so far is that since the side of the little squares are unknown, I called them "x", and so since the length of the full box is 12 inches, once folded up I'd have 12-2x. One thing I'm having trouble with is setting up my equation. I've done a similar problem before where it asks for volume, but I don't fully understand what it means by "side area." I also need to complete the perfect square to find dimension of the cut-out squares that result in largest possible side area.
 
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four sides, each with area $x(12-2x)$

therefore, total side area, $A = 4x(12-2x)$
 
I would be inclined to think that "side area" means "area of the sides" which is what what skeeter calculated.
 
If you interpret "largest side area" as meaning the area of one side, instead of all four, or the area of the four sides plus the bottom, you get the same answer so it really doesn't matter!
 
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