document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=341864>Question 341864</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The width of a rectangle is 8 less than twice its length. If the area of the rectangle is 200 cm^2, what is the length of the diagonal?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #244812 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=244812\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The width of a rectangle is 8 less than twice its length.<BR>\n" );
document.write( " If the area of the rectangle is 200 cm^2, what is the length of the diagonal?<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let x = the length<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(2x-8) = the width<BR>\n" );
document.write( "and<BR>\n" );
document.write( "x(2x-8) = 200; the area<BR>\n" );
document.write( "A quadratic equation<BR>\n" );
document.write( "2x^2 - 8x - 200 = 0<BR>\n" );
document.write( "Simplify, divide by 2<BR>\n" );
document.write( "x^2 - 4x - 100 = 0<BR>\n" );
document.write( "Find x using the quadratic formula<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 this equation: a=1; b=-4; c=-100<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-%28-4%29+%2B-+sqrt%28-4%5E2-4%2A1%2A-100+%29%29%2F%282%2A1%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-%28-4%29+%2B-+sqrt%28-4%5E2-4%2A1%2A-100+%29%29%2F%282%2A1%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+=+%284+%2B-+sqrt%2816+%2B+400+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%284+%2B-+sqrt%2816+%2B+400+%29%29%2F2+\"   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+=+%284+%2B-+sqrt%28416+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%284+%2B-+sqrt%28416+%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The positive solution is what we want here<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%284+%2B+20.4%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%284+%2B+20.4%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24.4%2F2 ALIGN=MIDDLE  ALT=\"24.4%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = 12.2 is the length<BR>\n" );
document.write( "then<BR>\n" );
document.write( "2(12.2) - 8 = 16.4 is the width<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Check solution by finding the area: 12.2 * 16.4 = 200.1 ~ 200, close enough<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Find the diagonal (d)<BR>\n" );
document.write( "d = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2812.2%5E2+%2B+16.4%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%2812.2%5E2+%2B+16.4%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "c = 20.44 cm is the diagonal<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );