document.write( "Question 242218: The area of the rectangular piece of cardboard shown on the left is 198 square inches. The cardboard is used to make an open box by cutting a 2 inch square from each corner and turning up the sides. If the box is to have a volume of 196 cubic inches, find the length and width of the cardboard that must be used. \n" ); document.write( "
Algebra.Com's Answer #177348 by ankor@dixie-net.com(22740)\"\" \"About 
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The area of the rectangular piece of cardboard shown on the left is 198 square inches.
\n" ); document.write( "The cardboard is used to make an open box by cutting a 2 inch square from each corner and turning up the sides.
\n" ); document.write( " If the box is to have a volume of 196 cubic inches, find the length and width of the cardboard that must be used.
\n" ); document.write( ":
\n" ); document.write( "Area of the original piece of cardboard
\n" ); document.write( "L * W = 198 sq/in
\n" ); document.write( "L = \"198%2FW\"
\n" ); document.write( ":
\n" ); document.write( "Volume L*W*H = 196 cu/in
\n" ); document.write( "(removing 2\" squares reduces the length and width by 4\", height = 2\"
\n" ); document.write( "(L-4)*(W-4)*2 = 196
\n" ); document.write( "Simplify, divide both sides by 2
\n" ); document.write( "(L-4)*(W-4) = 98
\n" ); document.write( "FOIL
\n" ); document.write( "LW - 4L - 4W + 16 = 98
\n" ); document.write( ":
\n" ); document.write( "LW - 4L - 4W + 16 - 98 = 0
\n" ); document.write( ":
\n" ); document.write( "LW - 4L - 4W - 82 = 0
\n" ); document.write( ":
\n" ); document.write( "From the area equation, replace L with 198/W
\n" ); document.write( "\"198%2FW\"*W - 4*\"198%2FW\" - 4W - 82 = 0
\n" ); document.write( "Cancel W, mult by 4
\n" ); document.write( "198 - \"792%2FW\" - 4W - 82 = 0
\n" ); document.write( ":
\n" ); document.write( "Mult by W to get rid of the denominator
\n" ); document.write( "198W - 792 - 4W^2 - 82W
\n" ); document.write( ":
\n" ); document.write( "Arrange as a quadratic equation
\n" ); document.write( "-4W^2 + 198W - 82W - 792 = 0
\n" ); document.write( ":
\n" ); document.write( "-4W^2 + 116W - 792 = 0
\n" ); document.write( "Divide by -2, simplify and change the signs
\n" ); document.write( "2W^2 - 58W + 396 = 0
\n" ); document.write( "This will factor
\n" ); document.write( "(2W - 22)(W - 18}) = 0
\n" ); document.write( "Two solutions
\n" ); document.write( "2W = 22
\n" ); document.write( "W = 11
\n" ); document.write( "and
\n" ); document.write( "W = 18
\n" ); document.write( ";
\n" ); document.write( "18\" by 11\" is the cardboard used
\n" ); document.write( ":
\n" ); document.write( "Check the area: 18 * 11 = 198
\n" ); document.write( ":
\n" ); document.write( "Check the vol of the box
\n" ); document.write( "(18-4)*(11-4)* 2 = 196\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
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