SOLUTION: A one compartment vertical file is to be constructed by bending the long side of an 8 inch by 20 inch sheet of plastic along two lines to form a U shape. How tall should the file b

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: A one compartment vertical file is to be constructed by bending the long side of an 8 inch by 20 inch sheet of plastic along two lines to form a U shape. How tall should the file b      Log On


   

Question 414015: A one compartment vertical file is to be constructed by bending the long side of an 8 inch by 20 inch sheet of plastic along two lines to form a U shape. How tall should the file be to maximize the volume that it can hold?
Answer by MathLover1(20855) About Me  (Show Source):
You can put this solution on YOUR website!

The answer you want is 20%2F3. Since the short side is 8, that's going to stay the same so you really don't have to worry about that.
The side thats 20" is going to be made into 3 sides, so you only have to figure out the maximum area for the side that's 20".
So you want to break 20 into 3 parts, which when multiplied together give you the largest product.
one part is 8in+ and two other could be 6in both
In this case you just use 20%2F3, which will give the file a total volume+of around V=+8%2A8%2A6=384in%5E3.
. How tall should the file be to maximize the volume that it can hold: 6in