Question 6611
Alright. We're cool with V = l * w * h, right, and we know that h = 3 and the volume is 60 in^2. So far we've got


{{{ 60 = l * w * 3 }}}


The trick is with the L and the W. You were right when you said that L = 2W. The length of the original sheet is twice the width of the original sheet BEFORE chopping of 3-inch by 3-inch squares on all four corners. When you chop off square corners, the actual length and width of the resulting folded box will definitely be shorter than the original L and W you started with.


Let's take the width. We decided to call it w. Now, when we cut off 3 inches from all 4 corners, that would actually chop 6 inches off the width. So the width of your box will have to be w - 6.


We know that the length = 2w BEFORE cutting off squares. Like the width, 3 inches were also chopped off the length from BOTH sides, making the actual length (of your box) 6 inches shorter. So the length of the box will be 2w - 6.


Let's now plug in the box's width and length:


{{{ 60 = (2w - 6)(w - 6)(3) }}} <----- We'll solve for the width eventually.


{{{ 20 = (2w - 6)(w - 6) }}} <----- Divided both sides by 3


{{{ 20 = 2w^2 - 18x + 36 }}} <----- Performed "FOIL"


{{{ 0 = 2w^2 - 18x + 16 }}} <----- Subtract 20 from both sides.


{{{ 0 = w^2 - 9x + 8 }}} <---- Divide both sides by 2


{{{ 0 = (w - 8)(w - 1) }}} <---- "UnFOILED" or factored


Just by looking at the above equation, the width is either 8 or 1. We'll have to throw out the 1 because that measure for the width won't work if you'll have to chop 6 inches off it. The 8 would, though. If 8 is the width, and the length is twice the width, then the length is 16. So you've got a sheet that was 16" x 8".