SOLUTION: An open box is to be constructed from a square piece of cardboard by removing a square of side 6 feet from each corner and turning up the edges. If the box is to hold 864 cubic fe

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: An open box is to be constructed from a square piece of cardboard by removing a square of side 6 feet from each corner and turning up the edges. If the box is to hold 864 cubic fe      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 845394: An open box is to be constructed from a square piece of cardboard by removing a square of side 6 feet from each corner and turning up the edges. If the box is to hold 864 cubic feet, what should be the dimensions of the sheet metal?
Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = the side length of the square of sheet metal.

The height will be 6, the length of the piece turned upward.
The length of the base will be x-2*6.

VOLUME: highlight_green%28%28x-12%29%28x-12%296=864%29.
6%28x-12%29%5E2=864
x%5E2-24x%2B144=864%2F6
x%5E2-24x%2B144=144
x%5E2-24x=0
x%28x-24%29=0
-
The acceptable answer is highlight%28x=24%29.
The uncut square sheet metal is 24 feet on each side.