document.write( "Question 78134This question is from textbook Elementary Algebra
\n" ); document.write( ": Constructing a box. I have a piece of cardboard that is twice as long as it is wide. If I cut a 2-inch by 2-inch square from each corner and fold up the resulting flaps, I get a box with a volume of 32 cubic inches. What are the dimensions of the cardboard? \n" ); document.write( "
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Constructing a box. I have a piece of cardboard that is twice as long as it is wide. If I cut a 2-inch by 2-inch square from each corner and fold up the resulting flaps, I get a box with a volume of 32 cubic inches. What are the dimensions of the cardboard?
\n" ); document.write( ":
\n" ); document.write( "Let x = the width
\n" ); document.write( "Then 2x = the length
\n" ); document.write( ":
\n" ); document.write( "If you draw this out, it will be apparent that the dimensions of the box are:
\n" ); document.write( "(x-4) by (2x-4) by 2
\n" ); document.write( ":
\n" ); document.write( "L * W * H = volume
\n" ); document.write( ":
\n" ); document.write( "(x-4)*(2x-4)* 2 = 32
\n" ); document.write( ":
\n" ); document.write( "2(2x^2 - 12x + 16) = 32
\n" ); document.write( ":
\n" ); document.write( "4x^2 - 24x + 32 - 32 = 0
\n" ); document.write( ":
\n" ); document.write( "4x^2 - 24x = 0
\n" ); document.write( ":
\n" ); document.write( "4x(x - 6) = 0
\n" ); document.write( ":
\n" ); document.write( "x = 0
\n" ); document.write( "and
\n" ); document.write( "x = +6 is the width, and 2(6) = 12 is the length
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "The dimension of the cardboard would be 6 by 12 by 2
\n" ); document.write( ":
\n" ); document.write( "Check the volume:
\n" ); document.write( "(6-4) * (12-4) * 2 =
\n" ); document.write( " 2 * 8 * 2 = 32
\n" ); document.write( " \n" ); document.write( "
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