SOLUTION: A rectangular piece of cardboard is 10 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 1132723: A rectangular piece of cardboard is 10 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 357 in3. Find the length and width of the piece of cardboard. Found 2 solutions by solver91311, greenestamps:Answer by solver91311(24713) (Show Source):
Let the width of the original piece of cardboard be represented by . Then represents the measure of the length of the original piece of cardboard. If 3-inch squares are cut from each corner, the width remaining for the bottom of the box must be and the length remaining for the bottom of the box must be . Since 3-inch squares were cut from the corners, the depth of the box when the sides are folded up must be 3 inches. Since the volume of the box is given by the depth of the box times the area of the bottom of the box, the area of the bottom of the box must be 357 cubic inches divided by 3 inches or 119 square inches. The area of the bottom of the box is the length of the bottom times the width of the bottom:
Solve the quadratic for the positive root which will be the width of the original piece of cardboard and then compute to find the length.
John
My calculator said it, I believe it, that settles it
The volume of the box is the area of the base multiplied by the height. The height is 3 inches, and the volume is 357 cubic inches; so the area of the base is 357/3 = 119 square inches.
Use mental arithmetic to find two numbers that differ by 10 and whose product is 119. Those will be the dimensions of the base of the box.
Then, since the box was formed by cutting 3-inch squares out of each corner of the original piece of cardboard, add 6 inches to each dimension of the base of the box to get the dimensions of the piece of cardboard.
