document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=204672>Question 204672</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you help me solve this question: 1)George is building a porch wrapped around his whole house. The dimensions of his house are 120m by 160m. If his porch is going to be the same area as his house, how wide will the porch be?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #154480 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=154480\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Can you help me solve this question: 1)George is building a porch wrapped around his whole house. The dimensions of his house are 120m by 160m. If his porch is going to be the same area as his house, how wide will the porch be?<BR>\n" );
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document.write( "Drawing a diagram of the problem will help you \"see\" how to approach it.<BR>\n" );
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document.write( "Let w = width of porch<BR>\n" );
document.write( "then<BR>\n" );
document.write( "\"area of house\" = \"area of porch<BR>\n" );
document.write( "120 * 160 =  [(120+2w)(160+2w)] - (120 * 160)<BR>\n" );
document.write( "19200 =  [(120+2w)(160+2w)] - 19200<BR>\n" );
document.write( "38400 =  (120+2w)(160+2w)<BR>\n" );
document.write( "38400 =  19200+240w+320w+4w^2<BR>\n" );
document.write( "0 =  -19200+560w+4w^2<BR>\n" );
document.write( "0 =  4w^2+560w-19200<BR>\n" );
document.write( "0 =  w^2+140w-4800<BR>\n" );
document.write( "Solve for w using the quadratic equation we get:<BR>\n" );
document.write( "w = {28.489, -168.489}<BR>\n" );
document.write( "Toss out the negative solution leaves us with:<BR>\n" );
document.write( "w = 28.489 meters<BR>\n" );
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document.write( "Details of quadratic to follow:<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=quadratic.solver>SOLVE quadratic equation with variable</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=aw%5E2%2Bbw%2Bc=0 ALIGN=MIDDLE  ALT=\"aw%5E2%2Bbw%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1w%5E2%2B140w%2B-4800+=+0 ALIGN=MIDDLE  ALT=\"1w%5E2%2B140w%2B-4800+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"w%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For these solutions to exist, the <U>discriminant</U> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be a negative number.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  First, we need to compute the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%28140%29%5E2-4%2A1%2A-4800=38800 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28140%29%5E2-4%2A1%2A-4800=38800\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=38800 is greater than zero. That means that there are two solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B12%5D+=+%28-140%2B-sqrt%28+38800+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-140%2B-sqrt%28+38800+%29%29%2F2%5Ca\"   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=w%5B1%5D+=+%28-%28140%29%2Bsqrt%28+38800+%29%29%2F2%5C1+=+28.488578017961 ALIGN=MIDDLE  ALT=\"w%5B1%5D+=+%28-%28140%29%2Bsqrt%28+38800+%29%29%2F2%5C1+=+28.488578017961\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%5B2%5D+=+%28-%28140%29-sqrt%28+38800+%29%29%2F2%5C1+=+-168.488578017961 ALIGN=MIDDLE  ALT=\"w%5B2%5D+=+%28-%28140%29-sqrt%28+38800+%29%29%2F2%5C1+=+-168.488578017961\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <BR>\n" );
document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1w%5E2%2B140w%2B-4800 ALIGN=MIDDLE  ALT=\"1w%5E2%2B140w%2B-4800\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be factored:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1w%5E2%2B140w%2B-4800+=+1%28w-28.488578017961%29%2A%28w--168.488578017961%29 ALIGN=MIDDLE  ALT=\"1w%5E2%2B140w%2B-4800+=+1%28w-28.488578017961%29%2A%28w--168.488578017961%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 28.488578017961, -168.488578017961.\n" );
document.write( "Here's your graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B140%2Ax%2B-4800+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B140%2Ax%2B-4800+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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