Question 1147587
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Without algebra....<br>
The volume is 18; and the height is 3, because the corners cut out of the piece of cardboard are 3x3 squares.<br>
Since volume is length times width times height, the product of the length and width is 18/3 = 6.<br>
If the original piece of cardboard is 5 inches longer than it is wide, then after the square pieces are cut off of each corner the bottom of the box will be 5 inches longer than it is wide.<br>
So we need two numbers that differ by 5 whose product is 6; those numbers, trivially, are 6 and 1.<br>
So the bottom of the box is 6x1 inches; since 3 inches in each direction were cut off of each corner of the original piece of cardboard, the dimensions of the original piece of cardboard were (6+6)x(1+6) = 12x7 inches.<br>