SOLUTION: A rectangular piece of cardboard has a total length that measures 6 inches more than its total width. A 2-inch by 2-inch square is cut out of each corner, and the remaining sides a

Question 296244: A rectangular piece of cardboard has a total length that measures 6 inches more than its total width. A 2-inch by 2-inch square is cut out of each corner, and the remaining sides are turned up at the dotted lines and their edges taped together to make a box with no top. The volume of the box is 110 cubic inches. What were the dimensions of the original piece of cardboard?
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
If L and W are the length and width, respectively, of the original piece of cardboard, and the cut-out corners are 2X2 inches, then the volume (V) of the newly-formed open top box with a height (h) of 2 inches can be expressed as:
Substitute
and the volume of this box is given as cu.in., so we can write:
Simplify and solve for W.
Divide both sides by 2.
Subtract 55 from both sides.
Solve by factoring.
so that...
or Discard the negative solution as the width W is a positive quantity.
inches. and...

inches.
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