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A rectangular piece of metal is 10 in longer than it is wide.
\n" ); document.write( " Squares with sides 2 in long are cut from the four corners and the flaps are folded upward to form an open box.
\n" ); document.write( " If the volume of the box is 528 in3, what were the original dimensions of the piece of metal?
\n" ); document.write( ":
\n" ); document.write( "let x = the width of the rectangular piece of metal
\n" ); document.write( "then
\n" ); document.write( "(x+10) = the length
\n" ); document.write( ":
\n" ); document.write( "Removing the 2\" squares would make the dimensions of the box:
\n" ); document.write( "(x-4) by (x+10-4) or (x-4) by (x+6)
\n" ); document.write( "the height of the box = 2\"
\n" ); document.write( ":
\n" ); document.write( "The volume equation L * W * h
\n" ); document.write( "(x+6)*(x-4)*2 = 528
\n" ); document.write( "divide both sides by 2
\n" ); document.write( "(x+6)(x-4) = 264
\n" ); document.write( "FOIL
\n" ); document.write( "x^2 - 4x + 6x - 24 = 264
\n" ); document.write( "x^2 + 2x - 24 - 264 = 0
\n" ); document.write( "a quadratic equation
\n" ); document.write( "x^2 + 2x - 288 = 0
\n" ); document.write( "You can use the quadratic formula a=1; b=2; c=-288, but this will factor to
\n" ); document.write( "(x+18)(x-16) = 0
\n" ); document.write( "the positive solution
\n" ); document.write( "x = 16 in is the width of the rectangular metal
\n" ); document.write( "then
\n" ); document.write( "26 in = the length
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Check this, the dimensions of the box will be 4' less and the length and width
\n" ); document.write( "22 * 12 * 2 = 528 cu in \n" ); document.write( "