document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=87998>Question 87998</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Would someone please show the solution to this word problem step by step. Thank you.<BR>\n" );
document.write( "The length of a rectangle is 1 cm longer than its width. If the diagonal of the rectangle is 4 cm. What are the dimensions (the length and the width) 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 #63884 by </B><A HREF=/tutors/aboutme.mpl?userid=tutor_paul><B>tutor_paul(519)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=tutor_paul><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=tutor_paul><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=63884\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The diagonal of the rectangle forms the hypoteneuse of a right triangle with the legs of said triangle being the length and the width of the rectangle. Wow, that<BR>\n" );
document.write( "was a mouthful. Anyways, they give you that l=w+1. So you can use the pythagorean theorem to write an equation for w:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28w%2B1%29%5E2%2Bw%5E2=4%5E2 ALIGN=MIDDLE  ALT=\"%28w%2B1%29%5E2%2Bw%5E2=4%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Square the binomial and simplify the right hand side:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%5E2%2B2w%2B1%2Bw%5E2=16 ALIGN=MIDDLE  ALT=\"w%5E2%2B2w%2B1%2Bw%5E2=16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Put the quadratic in standard form and combine like terms:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2w%5E2%2B2w-15=0 ALIGN=MIDDLE  ALT=\"2w%5E2%2B2w-15=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Use the quadratic formula:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=%28-2%2B-sqrt%28%284-%284%2A2%2A%28-15%29%29%29%29%29%2F4 ALIGN=MIDDLE  ALT=\"w=%28-2%2B-sqrt%28%284-%284%2A2%2A%28-15%29%29%29%29%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Simplify:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=%28-2%2B-sqrt%28%284-%28-120%29%29%29%29%2F4 ALIGN=MIDDLE  ALT=\"w=%28-2%2B-sqrt%28%284-%28-120%29%29%29%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=%28-2%2B-sqrt%28124%29%29%2F4 ALIGN=MIDDLE  ALT=\"w=%28-2%2B-sqrt%28124%29%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You need to have a positive value for the width, so throw away the negative result:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=%28-2%2B%282%29%2Asqrt%2831%29%29%2F4 ALIGN=MIDDLE  ALT=\"w=%28-2%2B%282%29%2Asqrt%2831%29%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Simplify a little more:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28w=%28-1%2Bsqrt%2831%29%29%2F2%29 ALIGN=MIDDLE  ALT=\"highlight%28w=%28-1%2Bsqrt%2831%29%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You can plug this into your calculator if you need a numerical value.<BR>\n" );
document.write( "from the given information, l is just 1+w.<BR>\n" );
document.write( "Good Luck,<BR>\n" );
document.write( "tutor_paul@yahoo.com<BR>\n" );
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