document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=871475>Question 871475</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a rectangular lawn has an area of 667 square meters. Surrounding the lawn is a flower border 4 meters wide. The border alone has an area of 548 square meters. <BR>\n" );
document.write( "A circular sprinkler is installed in the middle of the lawn. What is the spraying radius of the sprinkler if it covers the entire yard, including the flower border? <BR>\n" );
document.write( "Explain, in detail, all the reasoning, algebra, and problem-solving techniques you use to solve this problem. Represent all variables and include key steps and formulas you used. thank you for your help,\r<BR>\n" );
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document.write( "Harry<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #525539 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=525539\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Dimensions x and y.<BR>\n" );
document.write( " A diagonal is the size of the diameter of the sprinkler reach.\r<BR>\n" );
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document.write( "Lawn is xy=667.<BR>\n" );
document.write( "Flower border AND lawn is (x+2*4)(y+2*4)=(x+8)(y+8).<BR>\n" );
document.write( "Just the flower border is (x+8)(y+8)-xy=548, the value been given.\r<BR>\n" );
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document.write( "Simplify the border equation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xy%2B8x%2B8y%2B64-xy=548 ALIGN=MIDDLE  ALT=\"xy%2B8x%2B8y%2B64-xy=548\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x%2B8y=548 ALIGN=MIDDLE  ALT=\"8x%2B8y=548\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B2y=137 ALIGN=MIDDLE  ALT=\"2x%2B2y=137\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now we have a system of two equations in x and y.<BR>\n" );
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document.write( "xy=667<BR>\n" );
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document.write( "2x+2y=137<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y=137-2x ALIGN=MIDDLE  ALT=\"2y=137-2x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28137-2x%29%2F2 ALIGN=MIDDLE  ALT=\"y=%28137-2x%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "substititute.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28137-2x%29%2F2=667 ALIGN=MIDDLE  ALT=\"x%28137-2x%29%2F2=667\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2x%5E2%2B137x=2%2A667 ALIGN=MIDDLE  ALT=\"-2x%5E2%2B137x=2%2A667\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2x%5E2%2B137x=1334 ALIGN=MIDDLE  ALT=\"-2x%5E2%2B137x=1334\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2-137x%2B1334=0 ALIGN=MIDDLE  ALT=\"2x%5E2-137x%2B1334=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Check discriminant, 137^2-4*2*1334=18769-10672=8097<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28137%2B-+sqrt%288097%29%29%2F4 ALIGN=MIDDLE  ALT=\"x=%28137%2B-+sqrt%288097%29%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x=56.746 or x =11.754;<BR>\n" );
document.write( "resulting y,<BR>\n" );
document.write( "y=11.754 or y=56.746\r<BR>\n" );
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document.write( "Wanted was garden AND border, so staying with decimals, one dimension is 56.746+8 and other dimension is 11.754+8.  Those are 64.748 and 19.754.<BR>\n" );
document.write( "Diameter, same as the diagonal is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%2864.748%29%5E2%2B%2819.754%29%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28%2864.748%29%5E2%2B%2819.754%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >; and since question asks for the radius of this circular spray pattern area reached, the radius is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28sqrt%28%2864.748%29%5E2%2B%2819.754%29%5E2%29%2F2%29 ALIGN=MIDDLE  ALT=\"highlight%28sqrt%28%2864.748%29%5E2%2B%2819.754%29%5E2%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
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