document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=188725>Question 188725</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0395977258/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> a rectangular garden  has a perimeter of 44m.   A walkway 2m wide surrounds  the garden.  The combined area of the garden and walkway is 224m2.  What are the dimensions. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #141786 by </B><A HREF=/tutors/aboutme.mpl?userid=jojo14344><B>jojo14344(1513)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jojo14344><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=141786\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Tahoma\" size=1.5><BR>\n" );
document.write( "</pre><font size=4><b><BR>\n" );
document.write( "Let's picture out the garden wit the walkway.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-2%2C10%2C-2%2C6%2Cline%280%2C0%2C0%2C4%29%2Cline%280%2C4%2C8%2C4%29%2Cline%288%2C4%2C8%2C0%29%2Cline%288%2C0%2C0%2C0%29%2Cline%28-1%2C-1%2C-1%2C5%29%2Cline%28-1%2C5%2C9%2C5%29%2Cline%289%2C5%2C9%2C-1%29%2Cline%289%2C-1%2C-1%2C-1%29%2Cgreen%28arrow%284%2C4%2C4%2C5%29%29%2Cgreen%28arrow%284%2C0%2C4%2C-1%29%29%2Cgreen%28arrow%280%2C2%2C-1%2C2%29%29%2Cgreen%28arrow%288%2C2%2C9%2C2%29%29%2Clocate%28-.7%2C2.5%2C2m%29%2Clocate%288.3%2C2.5%2C2m%29%2Clocate%284.3%2C4.7%2C2m%29%2Clocate%284.3%2C-.3%2C2m%29%2Cgreen%28locate%283%2C2%2CGARDEN%29%29%2Cgreen%28arrow%285%2C4%2C6%2C5.5%29%29%2Cblue%28locate%285.5%2C6%2CPerimeter=44m%29%29%2Cblue%28locate%280%2C-.5%2CWalkway%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "We know for Rectangle, ---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Perimeter+=+2%28L%2BW%29 ALIGN=MIDDLE  ALT=\"Perimeter+=+2%28L%2BW%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, Eqn 1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=44m=2%28L%2BW%29 ALIGN=MIDDLE  ALT=\"44m=2%28L%2BW%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%2844%2922%2Fcross%282%29=cross%282%29%28L%2BW%29%2Fcross%282%29 ALIGN=MIDDLE  ALT=\"cross%2844%2922%2Fcross%282%29=cross%282%29%28L%2BW%29%2Fcross%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28L=22-W%29 ALIGN=MIDDLE  ALT=\"red%28L=22-W%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, Eqn 2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Also we know, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Area+=+L%2AW ALIGN=MIDDLE  ALT=\"Area+=+L%2AW\"   DISABLED_style= \"max-width:90%; height:auto;\" >, Eqn 3 \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now for the Combined Area (Garden + Walkway), we need to add \"4 meters\" for each Length and Width as shown.<BR>\n" );
document.write( "<font color=blue>New Length= L+2m+2m= L+4m; New Width= W+2m+2m = W+4m</font>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Then going back Eqn 3, for the combined Area:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=%28L%2B4%29%28W%2B4%29 ALIGN=MIDDLE  ALT=\"A=%28L%2B4%29%28W%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, substitute Eqn 2:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=224=%28highlight%2822-W%29%2B4%29%28W%2B4%29 ALIGN=MIDDLE  ALT=\"224=%28highlight%2822-W%29%2B4%29%28W%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=224=%2826-W%29%28W%2B4%29 ALIGN=MIDDLE  ALT=\"224=%2826-W%29%28W%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Expand right terms (multiply):<BR>\n" );
document.write( "First terms: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28highlight%2826%29-W%29%28highlight%28W%29%2B4%29=red%2826W%29 ALIGN=MIDDLE  ALT=\"%28highlight%2826%29-W%29%28highlight%28W%29%2B4%29=red%2826W%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Outer terms: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28highlight%2826%29-W%29%28W%2Bhighlight%284%29%29=red%28104%29 ALIGN=MIDDLE  ALT=\"%28highlight%2826%29-W%29%28W%2Bhighlight%284%29%29=red%28104%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Inner terms: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2826-highlight%28W%29%29%28highlight%28W%29%2B4%29=red%28-W%5E2%29 ALIGN=MIDDLE  ALT=\"%2826-highlight%28W%29%29%28highlight%28W%29%2B4%29=red%28-W%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Last terms: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2826-highlight%28W%29%29%28W%2Bhighlight%284%29%29=red%28-4W%29 ALIGN=MIDDLE  ALT=\"%2826-highlight%28W%29%29%28W%2Bhighlight%284%29%29=red%28-4W%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Adding all results in <font color=red>red</font> mark:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=224=highlight%2826W%2B104-W%5E2-4W%29 ALIGN=MIDDLE  ALT=\"224=highlight%2826W%2B104-W%5E2-4W%29\"   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%2B22W%2B104-224=0 ALIGN=MIDDLE  ALT=\"-W%5E2%2B22W%2B104-224=0\"   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%2B22W-120=0 ALIGN=MIDDLE  ALT=\"-W%5E2%2B22W-120=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, divide by \"-1\"  becomes---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W%5E2-22W%2B120=0 ALIGN=MIDDLE  ALT=\"W%5E2-22W%2B120=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, working eqn<BR>\n" );
document.write( "*Remember<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28a=1%2Cb=%28-22%29%2Cc=120%29 ALIGN=MIDDLE  ALT=\"system%28a=1%2Cb=%28-22%29%2Cc=120%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Solving discriminant: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=-22%5E2-4%281%29%28120%29=484-480=red%284%29 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=-22%5E2-4%281%29%28120%29=484-480=red%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Then, by quadratic:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W=x=%28-b%2B-sqrt%284%29%29%2F%282a%29=%28-%28-22%29%2B-2%29%2F%282%2A1%29=%2822%2B-2%29%2F2 ALIGN=MIDDLE  ALT=\"W=x=%28-b%2B-sqrt%284%29%29%2F%282a%29=%28-%28-22%29%2B-2%29%2F%282%2A1%29=%2822%2B-2%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=W=%2822%2B2%29%2F2=24%2F2=red%2812%29 ALIGN=MIDDLE  ALT=\"W=%2822%2B2%29%2F2=24%2F2=red%2812%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W=%2822-2%29%2F2=20%2F2=red%2810%29 ALIGN=MIDDLE  ALT=\"W=%2822-2%29%2F2=20%2F2=red%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Width of the Garden can either be <font color=red>W[1]=12m</font> or <font color=red>W[2]=10m</font>.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "For Length, go back Eqn 2:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=22-W=22-12=red%2810m%29 ALIGN=MIDDLE  ALT=\"L=22-W=22-12=red%2810m%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=22-W=22-10=red%2812m%29 ALIGN=MIDDLE  ALT=\"L=22-W=22-10=red%2812m%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Length can either be <font color=red>L[1]=10m</font> or <font color=red>L[2]=12m</font>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Let's check with the combined Area:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5BG%2BW%5D=+%28L%5B1%5D%2B4%29%28W%5B1%5D%2B4%29 ALIGN=MIDDLE  ALT=\"A%5BG%2BW%5D=+%28L%5B1%5D%2B4%29%28W%5B1%5D%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=224m%5E2=%2810%2B4%29%2812%2B4%29 ALIGN=MIDDLE  ALT=\"224m%5E2=%2810%2B4%29%2812%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=224m%5E2=%2814%29%2816%29 ALIGN=MIDDLE  ALT=\"224m%5E2=%2814%29%2816%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=224m%5E2=224m%5E2 ALIGN=MIDDLE  ALT=\"224m%5E2=224m%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Thank you,<BR>\n" );
document.write( "Jojo</font>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );