document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=107935>Question 107935</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The diagonal of a rectangle is 2 ft longer than its length and 5 feet longer than its width. What are the dimensions of the rectangle? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #78676 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=78676\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The diagonal of a rectangle is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2+ft ALIGN=MIDDLE  ALT=\"2+ft\"   DISABLED_style= \"max-width:90%; height:auto;\" > longer than its <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=length ALIGN=MIDDLE  ALT=\"length\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5+ft ALIGN=MIDDLE  ALT=\"5+ft\"   DISABLED_style= \"max-width:90%; height:auto;\" > longer than its <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=width ALIGN=MIDDLE  ALT=\"width\"   DISABLED_style= \"max-width:90%; height:auto;\" >. <BR>\n" );
document.write( "What are the dimensions of the rectangle?\r<BR>\n" );
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document.write( "Since the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=diagonal ALIGN=MIDDLE  ALT=\"diagonal\"   DISABLED_style= \"max-width:90%; height:auto;\" > divides rectangle into two <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=right ALIGN=MIDDLE  ALT=\"right\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=trianles ALIGN=MIDDLE  ALT=\"trianles\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we will use <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Pythagoras%27+ ALIGN=MIDDLE  ALT=\"Pythagoras%27+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Theorem+ ALIGN=MIDDLE  ALT=\"Theorem+\"   DISABLED_style= \"max-width:90%; height:auto;\" > in order to find the dimensions of the rectangle.\r<BR>\n" );
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document.write( "In algebraic terms, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a2+%2B+b2+=+c2 ALIGN=MIDDLE  ALT=\"a2+%2B+b2+=+c2\"   DISABLED_style= \"max-width:90%; height:auto;\" >where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the hypotenuse ( in your case the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=diagonal ALIGN=MIDDLE  ALT=\"diagonal\"   DISABLED_style= \"max-width:90%; height:auto;\" >) while <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+ ALIGN=MIDDLE  ALT=\"b+\"   DISABLED_style= \"max-width:90%; height:auto;\" >are the legs of the triangle (in your case the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=lenght ALIGN=MIDDLE  ALT=\"lenght\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=width ALIGN=MIDDLE  ALT=\"width\"   DISABLED_style= \"max-width:90%; height:auto;\" >).\r<BR>\n" );
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document.write( "given:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+=+a+%2B+2ft ALIGN=MIDDLE  ALT=\"c+=+a+%2B+2ft\"   DISABLED_style= \"max-width:90%; height:auto;\" >   => <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+c+%96+2ft ALIGN=MIDDLE  ALT=\"a+=+c+%96+2ft\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+=+b+%2B+5ft ALIGN=MIDDLE  ALT=\"c+=+b+%2B+5ft\"   DISABLED_style= \"max-width:90%; height:auto;\" >  =>  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+c+%96+5ft ALIGN=MIDDLE  ALT=\"b+=+c+%96+5ft\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "we will substitute it in:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2+=+a%5E2+%2B+b%5E2 ALIGN=MIDDLE  ALT=\"c%5E2+=+a%5E2+%2B+b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2+=+%28c-2ft%29%5E2+%2B+%28c-5ft%29%5E2 ALIGN=MIDDLE  ALT=\"c%5E2+=+%28c-2ft%29%5E2+%2B+%28c-5ft%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2+=+c%5E2+-4cft+%2B+4ft%5E2+%2B+c%5E2+%96+10cft+%2B+25ft%5E2 ALIGN=MIDDLE  ALT=\"c%5E2+=+c%5E2+-4cft+%2B+4ft%5E2+%2B+c%5E2+%96+10cft+%2B+25ft%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2+=+2c%5E2+%96+14cft+%2B29ft%5E2 ALIGN=MIDDLE  ALT=\"c%5E2+=+2c%5E2+%96+14cft+%2B29ft%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2+-14cft+%2B+29ft%5E2+=+0 ALIGN=MIDDLE  ALT=\"c%5E2+-14cft+%2B+29ft%5E2+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5B1%2C2%5D=%2814+%2B-+sqrt+%2814%5E2+-4%2A1%2A29+%29%29+%2F+%282%2A1%29 ALIGN=MIDDLE  ALT=\"c%5B1%2C2%5D=%2814+%2B-+sqrt+%2814%5E2+-4%2A1%2A29+%29%29+%2F+%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We need only positive root\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5B1%5D=%2814+%2B+sqrt+%2814%5E2+-4%2A1%2A29+%29%29+%2F+%282%2A1%29 ALIGN=MIDDLE  ALT=\"c%5B1%5D=%2814+%2B+sqrt+%2814%5E2+-4%2A1%2A29+%29%29+%2F+%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5B1%5D=%2814+%2B+sqrt+%28196-116++%29%29+%2F+2 ALIGN=MIDDLE  ALT=\"c%5B1%5D=%2814+%2B+sqrt+%28196-116++%29%29+%2F+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5B1%5D=%2814+%2B+sqrt+%2880%29%29+%2F+2 ALIGN=MIDDLE  ALT=\"c%5B1%5D=%2814+%2B+sqrt+%2880%29%29+%2F+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5B1%5D=%2814+%2B+8.9%29+%2F+2 ALIGN=MIDDLE  ALT=\"c%5B1%5D=%2814+%2B+8.9%29+%2F+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5B1%5D=%2822.9%29+%2F+2 ALIGN=MIDDLE  ALT=\"c%5B1%5D=%2822.9%29+%2F+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5B1%5D=%2811.45ft%29+ ALIGN=MIDDLE  ALT=\"c%5B1%5D=%2811.45ft%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+c+%96+2ft ALIGN=MIDDLE  ALT=\"a+=+c+%96+2ft\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+11.45ft+%96+2ft+=+9.45ft ALIGN=MIDDLE  ALT=\"a+=+11.45ft+%96+2ft+=+9.45ft\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+c+%96+5ft ALIGN=MIDDLE  ALT=\"b+=+c+%96+5ft\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+11.45ft+%96+5ft ALIGN=MIDDLE  ALT=\"b+=+11.45ft+%96+5ft\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+6.45ft ALIGN=MIDDLE  ALT=\"b+=+6.45ft\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Check:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2811.45%29%5E2+=+%289.45%29%5E2+%2B+%286.45%29%5E2 ALIGN=MIDDLE  ALT=\"%2811.45%29%5E2+=+%289.45%29%5E2+%2B+%286.45%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=131.1025+=+89.3025+%2B+41.6025 ALIGN=MIDDLE  ALT=\"131.1025+=+89.3025+%2B+41.6025\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=131+=+131 ALIGN=MIDDLE  ALT=\"131+=+131\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );