document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=205907>Question 205907</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help with this problem please: I found it on here but it is worded wrong.\r<BR>\n" );
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document.write( "Hazel has a screen door whose height is 4 feet more than its width. She wishes to stabilze the door by attaching a steel cable diagonally. If the cable measures sqrt194/2ft, what are the dimensions of the door?<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 #155470 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=155470\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hazel has a screen door whose height is 4 feet more than its width. She wishes to stabilze the door by attaching a steel cable diagonally. If the cable measures sqrt194/2ft, what are the dimensions of the door?<BR>\n" );
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document.write( "Let w = width of door<BR>\n" );
document.write( "then<BR>\n" );
document.write( "w+4 = length of door<BR>\n" );
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document.write( "From Pythagorean theorem we know:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+w%5E2+%2B+%28w%2B4%29%5E2+=+%28sqrt%28194%29%2F2%29%5E2+ ALIGN=MIDDLE  ALT=\"+w%5E2+%2B+%28w%2B4%29%5E2+=+%28sqrt%28194%29%2F2%29%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+w%5E2+%2B+%28w%5E2%2B8w%2B16%29+=+194%2F4+ ALIGN=MIDDLE  ALT=\"+w%5E2+%2B+%28w%5E2%2B8w%2B16%29+=+194%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2w%5E2+%2B+8w+%2B+16++=+194%2F4+ ALIGN=MIDDLE  ALT=\"+2w%5E2+%2B+8w+%2B+16++=+194%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+8w%5E2+%2B+16w+%2B+64++=+194+ ALIGN=MIDDLE  ALT=\"+8w%5E2+%2B+16w+%2B+64++=+194+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+8w%5E2+%2B+16w+-+130++=+0+ ALIGN=MIDDLE  ALT=\"+8w%5E2+%2B+16w+-+130++=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4w%5E2+%2B+8w+-+65+=+0+ ALIGN=MIDDLE  ALT=\"+4w%5E2+%2B+8w+-+65+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Applying the quadratic equation we get:<BR>\n" );
document.write( "w = {3.153, -5.153}<BR>\n" );
document.write( "Throwing out the negative solution we're left with:<BR>\n" );
document.write( "w = 3.153 feet (width)<BR>\n" );
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document.write( "Length:<BR>\n" );
document.write( "w+4 = 3.153 + 4 = 7.153 feet (length)<BR>\n" );
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document.write( "Details of quadratic:<BR>\n" );
document.write( "<TABLE  BORDER=1>\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=4w%5E2%2B8w%2B-65+=+0 ALIGN=MIDDLE  ALT=\"4w%5E2%2B8w%2B-65+=+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=%288%29%5E2-4%2A4%2A-65=1104 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%288%29%5E2-4%2A4%2A-65=1104\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=1104 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+=+%28-8%2B-sqrt%28+1104+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-8%2B-sqrt%28+1104+%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-%288%29%2Bsqrt%28+1104+%29%29%2F2%5C4+=+3.15331193145904 ALIGN=MIDDLE  ALT=\"w%5B1%5D+=+%28-%288%29%2Bsqrt%28+1104+%29%29%2F2%5C4+=+3.15331193145904\"   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-%288%29-sqrt%28+1104+%29%29%2F2%5C4+=+-5.15331193145904 ALIGN=MIDDLE  ALT=\"w%5B2%5D+=+%28-%288%29-sqrt%28+1104+%29%29%2F2%5C4+=+-5.15331193145904\"   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=4w%5E2%2B8w%2B-65 ALIGN=MIDDLE  ALT=\"4w%5E2%2B8w%2B-65\"   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=4w%5E2%2B8w%2B-65+=+4%28w-3.15331193145904%29%2A%28w--5.15331193145904%29 ALIGN=MIDDLE  ALT=\"4w%5E2%2B8w%2B-65+=+4%28w-3.15331193145904%29%2A%28w--5.15331193145904%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 3.15331193145904, -5.15331193145904.\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+4%2Ax%5E2%2B8%2Ax%2B-65+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B8%2Ax%2B-65+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "</TD></TR></TABLE>\n" );