document.write( "Question 186088: Thomas is going to make an open-top box by cutting equal squares from the four corners of an 11 inch by 14 inch sheet of a cardboard and folding up the sides. If the area of the base is to be 80 square inches then what size square should be cut from each corner? \n" ); document.write( "
Algebra.Com's Answer #139598 by ankor@dixie-net.com(22740)\"\" \"About 
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make an open-top box by cutting equal squares from the four corners of
\n" ); document.write( " an 11 inch by 14 inch sheet of a cardboard and folding up the sides.
\n" ); document.write( " If the area of the base is to be 80 square inches then what size square
\n" ); document.write( " should be cut from each corner?
\n" ); document.write( ";
\n" ); document.write( "Let x = the side of the square to cut from each corner
\n" ); document.write( ":
\n" ); document.write( "Draw a rough diagram of what is described, labeling the sides of the squares
\n" ); document.write( "as x and rectangular sheet as 11 by 14. It will be apparent to you that the
\n" ); document.write( "dimensions of the bottom of the box will be (11-2x) by (14-2x), which is given
\n" ); document.write( "as an area of 80 sq/in
\n" ); document.write( ":
\n" ); document.write( "(11-2x) * (14-2x) = 80
\n" ); document.write( "FOIL
\n" ); document.write( "154 - 22x - 28x + 4x^2 = 80
\n" ); document.write( "Arrange as a quadratic equation:
\n" ); document.write( "4x^2 - 50x + 154 - 80 = 0
\n" ); document.write( ":
\n" ); document.write( "4x^2 - 50x + 74 = 0
\n" ); document.write( "Simplify, divide by 2:
\n" ); document.write( "2x^2 - 25x + 37 = 0
\n" ); document.write( ":
\n" ); document.write( "Use the quadratic formula to find x
\n" ); document.write( "\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"
\n" ); document.write( "in this problem a=2, b=-25, c=37
\n" ); document.write( "\"x+=+%28-%28-25%29+%2B-+sqrt%28-25%5E2+-+4+%2A+2+%2A37+%29%29%2F%282%2A2%29+\"
\n" ); document.write( ":
\n" ); document.write( "\"x+=+%2825+%2B-+sqrt%28625+-+296+%29%29%2F%284%29+\"
\n" ); document.write( ":
\n" ); document.write( "\"x+=+%2825+%2B-+sqrt%28329%29%29%2F%284%29+\"
\n" ); document.write( "Two solutions
\n" ); document.write( "\"x+=+%2825+%2B+18.138%29%2F%284%29+\"
\n" ); document.write( "x = \"43.138%2F4\"
\n" ); document.write( "x = 10.784
\n" ); document.write( "and
\n" ); document.write( "\"x+=+%2825+-+18.138%29%2F%284%29+\"
\n" ); document.write( "x = \"6.862%2F4\"
\n" ); document.write( "x = 1.712 inch squares, This is the only solution that makes sense here.
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Check solution. 2 * 1.712 = 3.43, subtract from the original dimensions and
\n" ); document.write( "find the area
\n" ); document.write( "(11-3.43) * (14-3.43) =
\n" ); document.write( "7.57 * 10.57 = 80.0 sq/in confirms our solution \n" ); document.write( "
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