SOLUTION: A rectangular piece of cardboaard is 2 units longer than it is wide. From each of its corners a square piece 2 units on a side is cut out. The flaps are then turned up to form an
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Question 184616This question is from textbook Elem. Algebra & Intermediate Algebra
: A rectangular piece of cardboaard is 2 units longer than it is wide. From each of its corners a square piece 2 units on a side is cut out. The flaps are then turned up to form an open box that has a volume of 70 cubic units. Find the length and width of the original piece of cardboard.
box volume = length x width x height
volume = 70
width = w
length = 2w (2 times the width)
height = 2
box volume would be 70=(x)(2w)(2)???
this gives me 70=4w^2??? this seems very difficult to work with, can you help me figure this problem out? Thank you.
This question is from textbook Elem. Algebra & Intermediate Algebra
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
You need to re-read your problem. The problem says that the length is 2 units longer than the width, not 2 times the width. Furthermore, the width of the box formed is 4 inches less than the original width of the cardboard, and the length of the box formed is 4 inches less than the original length of the cardboard because of the 2 inch squares cut out of the corners before the box was folded. So width is 
, length is 
, and height is 2.
So:
(w - 2) = 70 \ \ \Rightarrow\ \ 2w^2 - 12w + 16 - 70 = 0 \ \ \Rightarrow\ \ w^2 - 6w - 27 = 0)
Note: 
and 
so this factors neatly. One of your roots will be negative. Discard this extraneous root because it would be absurd to have a negative measure of length. The positive root is your width of the original cardboard and the length is two inches longer.
John
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