Question 1089094: The length of a rectangular piece of cardboard is 15 inches longer than its width. If a 5 inch square is cut from each corner of the cardboard, and the remaining piece is folded up to form a box, the volume of the box is 2,250 cubic inches. Find the sum of the length and the width, in inches, of the original cardboard.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! width is x
length is x+15
after cutting the 5 inch square, which involved both length and width twice
x-10 and x+5 are the dimensions
5 is the height
the volume is (x^2-5x-50)*5=2250
divide by 5 both sides
x^2-5x-50=450
x^2-5x-500=0
(x-25)(x+20)=0
x=25 inches, only positive root, original width.
x+15=40 inches, original length.
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Check.
Box is 15 inches wide by 30 inches long by 5 inches high, and that is a volume of 2250 in^3.
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