![\"\"](\"/images/stars/stars-13.gif\")
You can put this solution on YOUR website!
The area of the rectangular piece of cardboard shown below is 216 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 224 cubic inches, find the length and width of the cardboard that must be used.
\n" ); document.write( ":
\n" ); document.write( "Let L = the length of the box
\n" ); document.write( "then
\n" ); document.write( "(L+4) = the length of the piece cardboard (because of the 2\" squares)
\n" ); document.write( "and
\n" ); document.write( "Let W = the width of the box
\n" ); document.write( "then
\n" ); document.write( "(W+4) = the width of the cardboard
\n" ); document.write( ":
\n" ); document.write( "From the information given we know the height of the box will be 2\", therefore
\n" ); document.write( "the area of the bottom of the box will be: 224/2 = 112 sq/in
\n" ); document.write( "L*W = 112
\n" ); document.write( "and
\n" ); document.write( "(L+4)*(W+4) = 216, the area of the cardboard
\n" ); document.write( "FOIL
\n" ); document.write( "LW + 4L + 4W + 16 - 216 = 0
\n" ); document.write( "LW + 4L + 4W - 200 = 0
\n" ); document.write( "Replace LW with 112
\n" ); document.write( "112 + 4L + 4W - 200 = 0
\n" ); document.write( "4L + 4W - 200 + 112 = 0
\n" ); document.write( "4L + 4W - 88 = 0
\n" ); document.write( "simplify, divide by 4
\n" ); document.write( "L + W - 22 = 0
\n" ); document.write( "L + W = 22
\n" ); document.write( "L = (22-W)
\n" ); document.write( "Replace L with (22-W) in the area of the base equation
\n" ); document.write( "(22-W)*W = 112
\n" ); document.write( "-W^2 + 22W = 112
\n" ); document.write( "Arrange as a quadratic equation on the right
\n" ); document.write( "0 = W^2 - 22W + 112
\n" ); document.write( "Factors to
\n" ); document.write( "(W-8)(W-14) = 0
\n" ); document.write( "Two solutions
\n" ); document.write( "W = 8, then L = 14
\n" ); document.write( "W = 14, then L = 8
\n" ); document.write( ":
\n" ); document.write( "The box is 14 by 8 by 2, check volume: 14*8*2 = 224 cu/in
\n" ); document.write( ";
\n" ); document.write( "We add 4\" to the length and width of the cardboard: 18\" by 12\".
\n" ); document.write( "Check the area: 18*12 = 216 sq/in
\n" ); document.write( ":
\n" ); document.write( "Could you follow all this? Did I make it understandable to you? C\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "