document.write( "Question 328356: Box Construction. An open box is to be made from a 10-ft by 20-ft rectangular piece of cardboard by cutting a square from each corner. The area of the bottom of the box is to be 96ft^2. What is the length of the sides of the squares that are cut from the corners? \n" ); document.write( "
Algebra.Com's Answer #235346 by ankor@dixie-net.com(22740)\"\" \"About 
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An open box is to be made from a 10-ft by 20-ft rectangular piece of cardboard by cutting a square from each corner.
\n" ); document.write( " The area of the bottom of the box is to be 96ft^2.
\n" ); document.write( "What is the length of the sides of the squares that are cut from the corners?
\n" ); document.write( ":
\n" ); document.write( "let x = length of the sides of the removed squares
\n" ); document.write( ":
\n" ); document.write( "Then the dimensions of the box will be: (10-2x) by (20-2x) by x
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\n" ); document.write( "The area of the bottom is given as 96 sq/ft
\n" ); document.write( "therefore:
\n" ); document.write( "(10-2x)*(20-2x) = 96
\n" ); document.write( "FOIL
\n" ); document.write( "200 - 20x - 40x + 4x^2 = 96
\n" ); document.write( "Arrange as a quadratic equation
\n" ); document.write( "4x^2 - 60x + 200 - 96 = 0
\n" ); document.write( "4x^2 - 60x + 104 = 0
\n" ); document.write( "Simplify, divide by 4
\n" ); document.write( "x^2 - 15x + 26 = 0
\n" ); document.write( "Factors to
\n" ); document.write( "(x-13)(x-2) = 0
\n" ); document.write( "Two solutions
\n" ); document.write( "x = 13 ft, does not make sense
\n" ); document.write( "and
\n" ); document.write( "x = 2 ft, is the length of the side of the removed squares
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Check solution by finding the area:
\n" ); document.write( "[10 - 2(2)] * [20 - 2(2)] =
\n" ); document.write( "6 * 16 = 96\r
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