document.write( "Question 1200523: an open-topped box is constructed from a rectangular piece of cardboard that is twice as long as it is wide by removing a square of size 3 inches from each corner and turning up the edges. If the box is to hold 5,940 in^3, how big should the original piece of cardboard be? \n" ); document.write( "
Algebra.Com's Answer #834682 by Theo(13342)\"\" \"About 
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let L = the length and W equal the width of the rectangular piece of cardboard.
\n" ); document.write( "when you cut out 3 inch square from each corner of the cardboard, and fold up 3 inches from the length and the width, you are left with an open box that has the following dimensions.
\n" ); document.write( "length = L - 6
\n" ); document.write( "width = W - 6
\n" ); document.write( "height = 3
\n" ); document.write( "the volume of the open top box is equal to length * width * height which is equal to (L - 6) * (W - 6) * 3
\n" ); document.write( "since the length of the box is twice as long as it is wide, then you get L = 2W and the dimensions of the open top box are (2W - 6) * (W - 6) * 3
\n" ); document.write( "simplify this to get 2W * (W - 6) - 6 * (W - 6) * 3
\n" ); document.write( "simplify further to get (2W^2 - 12W - 6W + 36) * 3
\n" ); document.write( "simplify further to get 6W^2 - 36W - 18W + 108
\n" ); document.write( "combine like terms to get 6W^2 - 54W + 108
\n" ); document.write( "that's the volume of the open top box.
\n" ); document.write( "since the volume is 5940 cubic inches, you get:
\n" ); document.write( "6W^2 - 54W + 108 = 5940
\n" ); document.write( "subtract 5940 from both sides of the equation to get:
\n" ); document.write( "6W^2 - 54W - 5832 = 0
\n" ); document.write( "divide both sides of this equation by 6 to get:
\n" ); document.write( "W^2 - 54W - 972 = 0
\n" ); document.write( "factor this quadratic eqution to get:
\n" ); document.write( "W = -27 or plus 36.
\n" ); document.write( "W can't be negative, you are left with W = 36
\n" ); document.write( "since length is twice the width, you have:
\n" ); document.write( "W = 36
\n" ); document.write( "L = 72
\n" ); document.write( "the dimensions of the open top box are:
\n" ); document.write( "length = L - 6 = 66
\n" ); document.write( "width = W - 6 = 30
\n" ); document.write( "height = 3
\n" ); document.write( "the volume of the open top box is therefore 66 * 30 * 3 = 5940 cubic inches.
\n" ); document.write( "the original piece of cardboard should have a length of 36 and a width of 72.
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