document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=184287>Question 184287</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The length of a rectangular frame is 7cm more than the width. The area inside the the frame is 98 square cm. Find the width of the frame. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #138309 by </B><A HREF=/tutors/aboutme.mpl?userid=MathGuyJoe><B>MathGuyJoe(20)</B></A><img src=\"/images/stars/stars-06.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathGuyJoe><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=138309\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let L = Length of rectangle<BR>\n" );
document.write( "Let W = Width of rectangle<BR>\n" );
document.write( "<br><BR>\n" );
document.write( "We know:  \"The length of a rectangular frame (L) is (=) 7cm more than (+) the width (W)\" -> Equation 1: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+L+=+7+%2B+W+ ALIGN=MIDDLE  ALT=\"+L+=+7+%2B+W+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "We also know:  \"The area inside the frame (L x W) is (=) 98 square cm\" -> Equation 2: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+LW+=+98+ ALIGN=MIDDLE  ALT=\"+LW+=+98+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<br><BR>\n" );
document.write( "Next, we can use Equation 1 to substitute (7 + W) for L in Equation 2:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+LW+=+98+ ALIGN=MIDDLE  ALT=\"+LW+=+98+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substitute:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%287%2BW%29W+=+98+ ALIGN=MIDDLE  ALT=\"+%287%2BW%29W+=+98+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Distribute the W:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+7W+%2B+W%5E2+=+98+ ALIGN=MIDDLE  ALT=\"+7W+%2B+W%5E2+=+98+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Move everything to the left-hand side:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+W%5E2+%2B+7W+-+98+=+0+ ALIGN=MIDDLE  ALT=\"+W%5E2+%2B+7W+-+98+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Factor the quadratic:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28W+%2B+14%29%28W+-+7%29+=+0+ ALIGN=MIDDLE  ALT=\"+%28W+%2B+14%29%28W+-+7%29+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Solve:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W+%2B+14+=+0 ALIGN=MIDDLE  ALT=\"W+%2B+14+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W-7=+0 ALIGN=MIDDLE  ALT=\"W-7=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W+=+-14 ALIGN=MIDDLE  ALT=\"W+=+-14\"   DISABLED_style= \"max-width:90%; height:auto;\" >       <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W+=+7 ALIGN=MIDDLE  ALT=\"W+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<br><BR>\n" );
document.write( "Since a width cannot be negative, that leaves us with <b>Width = 7cm</b>.<BR>\n" );
document.write( "To check our answer, calculate our length by substituting back into Equation 1:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+L+=+W+%2B+7+ ALIGN=MIDDLE  ALT=\"+L+=+W+%2B+7+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+L+=+7+%2B+7+ ALIGN=MIDDLE  ALT=\"+L+=+7+%2B+7+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+L+=+14+ ALIGN=MIDDLE  ALT=\"+L+=+14+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Next, ensure the area is 98 square cm:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+LW+=+98+ ALIGN=MIDDLE  ALT=\"+LW+=+98+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%2814%29%287%29+=+98+ ALIGN=MIDDLE  ALT=\"+%2814%29%287%29+=+98+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+98+=+98+ ALIGN=MIDDLE  ALT=\"+98+=+98+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<br><BR>\n" );
document.write( "Hope this helps. ~ Joe </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );