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09032012  #1 
Join Date: Sep 2012
Posts: 1

volume of a box
Help!!
A large box has a volume of 180ft^3. Its length is 9ft greater than its height and its width is 4ft less than its height. What are the dimensions of the box? I have 180=(h+9)(h4)(h) and I keep coming up with h=4 which would mean the height is 0...not possible. Help!! 
09122012  #2  
Join Date: Dec 2008
Posts: 249

Quote:
(h^2 + 9h)(h  4) = 180 h^3  4h^2 + 9h^2  36h = 180 h^3 + 5h^2  36h = 180 h^3 + 5h^2  36h  180 = 0 Let's try 6 as a solution. (6)^3 + 5(6)^2  36(6)  180 = 0 216 + 180  216  180 = 0 0 = 0 It turns out the other 2 roots are 6 and 5 (you can check by plugging them into the equation) so we will use h = 6 ft for the height. Then the length is 6 + 9 = 15 ft and width is 6  4 = 2 ft. Hope this helps. 

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