SOLUTION: A box with no top is to be constructed from a piece of cardboard whose length measures 9 in. more than its width. The box is to be formed by cutting squares that measure 4 in. on e

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Question 1160912: A box with no top is to be constructed from a piece of cardboard whose length measures 9 in. more than its width. The box is to be formed by cutting squares that measure 4 in. on each side from the four corners and then folding up the sides. If the volume of the box will be 144 in.cubed​, what are the dimensions of the piece of​ cardboard?
Found 2 solutions by ikleyn, Edwin McCravy:
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.

From the condition, the height of the box is 4 inches;

therefore, the area of its base is   = 36 square inches.


If w is the width of the original cardboard in inches, then its length is (w+9) inches.


The dimensions of the base of the box are then  (w-2*4) = (w-8) inches and (w+9-2*4) = (w+1) inches.


So you have this equation for the base area


    (w-8)*(w+1) = 36.


Simplify and solve


    w^2 - 8w + w - 8 = 36

    w^2 - 7w - 44 = 0.

     =  =  = .


Only positive root  w =  = 11 makes sense.


ANSWER.  The original cardboard dimensions are  11 inches and 20 inches.

Solved.



Answer by Edwin McCravy(20055)   (Show Source): You can put this solution on YOUR website!
Here's the picture for Ikleyn's solution.  She beat me posting.
The width is w, and the length is w+9 inches.  We cut out the 
4 green 4 in. by 4 in. squares at the corners and fold up the 
sides and tape the edges to make an open-top box 4 inches high. 



Edwin
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