document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=902060>Question 902060</A>: <I><SPAN STYLE=\"word-break: break-all;\"> use a guess and check table:\r<BR>\n" );
document.write( "\n" );
document.write( "Devin grew a rectangle on graph paper. The area of the rectangle is 810 square centimeters. The length is 3 centimeters greater than the width. Find the length and 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 #547066 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=547066\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \"Guess and check table\"?  One of the reasons for learning basic algebra is to be able to solve numerical problems more efficiently than guessing and checking.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "L for length<BR>\n" );
document.write( "w for width<BR>\n" );
document.write( "L=w+3 and wL=810\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%3E0 ALIGN=MIDDLE  ALT=\"w%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and .... that will be the only restriction for now.<BR>\n" );
document.write( "Natural numbers will be used for the table, just for convenience although other real positive numbers would not be expected necessary.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "w____________L____________AREA, w*L<BR>\n" );
document.write( "_1____________4____________4<BR>\n" );
document.write( "_2____________5____________10<BR>\n" );
document.write( "_3____________6____________18<BR>\n" );
document.write( ".<BR>\n" );
document.write( "15___________18___________270<BR>\n" );
document.write( "20___________23___________460<BR>\n" );
document.write( "You can keep going this way until you find what you need.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "That is an inferior way to find the dimensions when you understand the geometry and the number properties well enough.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "__________________THE BETTR WAY____________________________\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "L=w+3, and w, the dimensions;<BR>\n" );
document.write( "and wL=810.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%28w%2B3%29=810 ALIGN=MIDDLE  ALT=\"w%28w%2B3%29=810\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%5E2%2B3w-810=0 ALIGN=MIDDLE  ALT=\"w%5E2%2B3w-810=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Try to factorize 810.<BR>\n" );
document.write( "810=10*81=2*5*9*9, but a list of all factors might be better.<BR>\n" );
document.write( "ALL FACTORS:  2, 3 , 5, 6, 9, 10, 15, 18, 27, 30 45, 54, 81, 90, 135,  162,  270,  405;<BR>\n" );
document.write( "The possible factorization which might work is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=27%2A30 ALIGN=MIDDLE  ALT=\"27%2A30\"   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=%28w-27%29%28w%2B30%29=0 ALIGN=MIDDLE  ALT=\"%28w-27%29%28w%2B30%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The meaningful solution here is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28w=27%29 ALIGN=MIDDLE  ALT=\"highlight%28w=27%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=w%2B3=27%2B3=highlight%2830%29 ALIGN=MIDDLE  ALT=\"L=w%2B3=27%2B3=highlight%2830%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );