document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=686696>Question 686696</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am not understanding how to start this word problem. We are supposed to be using quadratic equations. The problem is.....<BR>\n" );
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document.write( "     The length of a rectangle is 1cm more than twice it's width and 2cm less than the length of the diagonal of the rectangle. Find the dimensions of the rectangle.\r<BR>\n" );
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document.write( "I think the diagonal part is confusing me because we have never solved a problem with diagonal before.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #424890 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=424890\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The length of a rectangle is 1cm more than twice it's width and 2cm less than the length of the diagonal of the rectangle.<BR>\n" );
document.write( " Find the dimensions of the rectangle.<BR>\n" );
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document.write( "Let a = the width<BR>\n" );
document.write( "Let b = the length<BR>\n" );
document.write( "Let c = the diagonal<BR>\n" );
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document.write( "Write an equation for each statement, get each equation in terms of a:<BR>\n" );
document.write( "\"The length of a rectangle is 1cm more than twice it's width\"<BR>\n" );
document.write( "b = 2a + 1<BR>\n" );
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document.write( "\"the length is 2cm less than the length of the diagonal of the rectangle.\"<BR>\n" );
document.write( "b = c - 2<BR>\n" );
document.write( "replace b with (2a+1)<BR>\n" );
document.write( "2a + 1 = c - 2<BR>\n" );
document.write( "2a + 1 + 2 = c<BR>\n" );
document.write( "c = 2a + 3<BR>\n" );
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document.write( "The diagonal is the hypotenuse (c) of the rectangle where <BR>\n" );
document.write( "a^2 + b^2 = c^2<BR>\n" );
document.write( "Replace b with (2a+1) and replace c with (2a+3)<BR>\n" );
document.write( "a^2 + (2a+1)^2  = (2a+3)^2<BR>\n" );
document.write( "FOIL<BR>\n" );
document.write( "a^2 + 4a^2 + 2a + 2a + 1 = 4a^2 + 6a + 6a + 9<BR>\n" );
document.write( "Which is<BR>\n" );
document.write( "5a^2 + 4a + 1 = 4a^2 + 12a + 9<BR>\n" );
document.write( "Combine like terms on the left<BR>\n" );
document.write( "5a^2 - 4a^2 + 4a - 12a + 1 - 9 = 0<BR>\n" );
document.write( "a^2 - 8a - 8 = 0<BR>\n" );
document.write( "Solve this quadratic equation 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( "where x = a; b = -8; c = -8<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+%28-%28-8%29+%2B-+sqrt%28-8%5E2-4%2A1%2A-8+%29%29%2F%282%2A1%29+ ALIGN=MIDDLE  ALT=\"a+=+%28-%28-8%29+%2B-+sqrt%28-8%5E2-4%2A1%2A-8+%29%29%2F%282%2A1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+%288+%2B-+sqrt%2864%2B32+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"a+=+%288+%2B-+sqrt%2864%2B32+%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+%288+%2B-+sqrt%2896%29%29%2F2+ ALIGN=MIDDLE  ALT=\"a+=+%288+%2B-+sqrt%2896%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "two solutions but we only need the positive solution which is approx<BR>\n" );
document.write( "a = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288+%2B+9.8%29%2F2 ALIGN=MIDDLE  ALT=\"%288+%2B+9.8%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=17.8%2F2 ALIGN=MIDDLE  ALT=\"17.8%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a = 8.9 cm is the width<BR>\n" );
document.write( "then<BR>\n" );
document.write( "b = 2(8.9) + 1<BR>\n" );
document.write( "b = 18.8 cm is the length<BR>\n" );
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document.write( "Check this by finding the hypotenuse<BR>\n" );
document.write( "c = 2(8.9) + 3<BR>\n" );
document.write( "c = 20.8<BR>\n" );
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document.write( "Enter into calc <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%288.9%5E2+%2B+18.8%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%288.9%5E2+%2B+18.8%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > results: 20.800 confirms our solution<BR>\n" );
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document.write( " Find the dimensions of the rectangle. 18.8 by 8.9  </SPAN>\n" );
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