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

#### obesiston

##### New member
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 dont 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.

#### skeeter

##### Well-known member
MHB Math Helper
four sides, each with area $x(12-2x)$

therefore, total side area, $A = 4x(12-2x)$

#### HallsofIvy

##### Well-known member
MHB Math Helper
I would be inclined to think that "side area" means "area of the sides" which is what what skeeter calculated.

#### Country Boy

##### Well-known member
MHB Math Helper
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!