SOLUTION: A rectangular piece of cardboard is 12 in. longer than it is wide. Squares 3 in. on a side are to be cut from each corner, and then the sides will be folded up to make an open box
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-> SOLUTION: A rectangular piece of cardboard is 12 in. longer than it is wide. Squares 3 in. on a side are to be cut from each corner, and then the sides will be folded up to make an open box
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Question 1146037: A rectangular piece of cardboard is 12 in. longer than it is wide. Squares 3 in. on a side are to be cut from each corner, and then the sides will be folded up to make an open box with a volume of 135 in3. Find the length and width of the piece of cardboard. Answer by greenestamps(13200) (Show Source):
The volume of the box is length times width times height. The height is 3 inches, and the volume is 135 cubic inches. So the length times the width is 135/3 = 45.
When the 3-inch square pieces are cut out of each corner, the new length is still 12 inches more than the new width.
So we can solve the problem simply by finding two numbers that differ by 12 and whose product is 45.
A bit of mental arithmetic shows those two numbers to be 3 and 15. Then, since 3-inch square pieces were cut out of each corner of the piece of cardboard, the dimensions of the piece of cardboard were 3+6=9 and 15+6=21.
ANSWER: The piece of cardboard was 21x9 inches.
You can, of course, solve the problem using formal algebra.
x = width
x+12 = length
The volume is 135 after cutting out 3-inch squares from each corner:
