document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=332832>Question 332832</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Open-top box.Thomas is going to make an open-top box by cutting equal squares from the four corners of an 11inch by 14inch sheet of 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? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #238545 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=238545\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Open-top box.Thomas is going to make an open-top box by cutting equal squares<BR>\n" );
document.write( " from the four corners of an 11inch by 14inch sheet of cardboard and folding<BR>\n" );
document.write( " up the sides.<BR>\n" );
document.write( "If the area of the base is to be 80 square inches,<BR>\n" );
document.write( " then What size square should be cut from each corner?<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let x = side of the removed squares<BR>\n" );
document.write( "then<BR>\n" );
document.write( "Base dimensions: (11-2x) by (14-2x)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Area of base:<BR>\n" );
document.write( "(11-2x)*(14-2x) = 80<BR>\n" );
document.write( "FOIL<BR>\n" );
document.write( "154 - 22x - 28x + 4x^2 = 80<BR>\n" );
document.write( "Arrange as a quadratic equation<BR>\n" );
document.write( "4x^2 - 50x + 154 - 80 = 0<BR>\n" );
document.write( "4x^2 - 50x + 74 = 0<BR>\n" );
document.write( "Simplify, divide by 2<BR>\n" );
document.write( "2x^2 - 25x + 37 = 0<BR>\n" );
document.write( "use the quadratic formula to find x<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "in our equation, a=2, b=-25, c= 37<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-%28-25%29+%2B-+sqrt%28-25%5E2-4%2A2%2A37+%29%29%2F%282%2A2%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-%28-25%29+%2B-+sqrt%28-25%5E2-4%2A2%2A37+%29%29%2F%282%2A2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2825+%2B-+sqrt%28625-296+%29%29%2F4+ ALIGN=MIDDLE  ALT=\"x+=+%2825+%2B-+sqrt%28625-296+%29%29%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2825+%2B-+sqrt%28329+%29%29%2F4+ ALIGN=MIDDLE  ALT=\"x+=+%2825+%2B-+sqrt%28329+%29%29%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Two solutions<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2825+%2B+18.138%29%2F4+ ALIGN=MIDDLE  ALT=\"x+=+%2825+%2B+18.138%29%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=43.138%2F4 ALIGN=MIDDLE  ALT=\"43.138%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = 10.78<BR>\n" );
document.write( "and this is the solution that makes sense<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2825+-+18.138%29%2F4+ ALIGN=MIDDLE  ALT=\"x+=+%2825+-+18.138%29%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6.862%2F4 ALIGN=MIDDLE  ALT=\"6.862%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = 1.7 inches is the side of the removed squares<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Check by finding the area<BR>\n" );
document.write( "(11-2(1.7)) * (14-2(1.7)) = 80.56 ~ 80<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );