document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=343296>Question 343296</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A rectangular piece of matal is 10 in. longer than it is woide. Squares with sides 2 in. lon are cut from the four corners, and the flaps are folded upward to form an open box. if the volume of the box is 832 in3(to the third power) whaqt were the original dimensions of the piece of metal? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #245837 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=245837\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A rectangular piece of metal is 10 in. longer than it is wide.<BR>\n" );
document.write( " Squares with sides 2 in. long are cut from the four corners, and the flaps are<BR>\n" );
document.write( " folded upward to form an open box.<BR>\n" );
document.write( " if the volume of the box is 832 in3(to the third power) what were the original dimensions of the piece of metal?<BR>\n" );
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document.write( "We know the height of the box = 2\", therefore<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=832%2F2 ALIGN=MIDDLE  ALT=\"832%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 416 sq/in is the area of the base<BR>\n" );
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document.write( "Let x = the width of the metal<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(x+10) = the length of the metal<BR>\n" );
document.write( "Therefore<BR>\n" );
document.write( "dimensions of the box:<BR>\n" );
document.write( "(x-4) = the width<BR>\n" );
document.write( "and<BR>\n" );
document.write( "(x+10-4) = (x+6) the length of the box<BR>\n" );
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document.write( "Use the area of the base to find x:<BR>\n" );
document.write( "(x-4)*(x+6) = 416<BR>\n" );
document.write( "FOIL<BR>\n" );
document.write( "x^2 + 6x - 4x - 24 = 416<BR>\n" );
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document.write( "x^2 + 2x - 24 - 416 = 0<BR>\n" );
document.write( "a quadratic equation<BR>\n" );
document.write( "x^2 + 2x - 440 = 0<BR>\n" );
document.write( "Factor <BR>\n" );
document.write( "(x+22)(x-20) = 0<BR>\n" );
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document.write( "the positive solution is what we want here<BR>\n" );
document.write( "x = 20 in is the width of the metal<BR>\n" );
document.write( "and<BR>\n" );
document.write( "20 + 10 = 30 in is the length of the metal<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Check solution by finding the volume using these dimensions<BR>\n" );
document.write( "(20-4)*(30-4) * 2 = 832 cu/in, confirms our solution<BR>\n" );
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document.write( "20\" by 30\" is the dimensions of the metal </SPAN>\n" );
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