document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1049197>Question 1049197</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The parks department is planning a new flower bed outside city hall. It will be rectangular with dimensions 9m by 6m. The flower bed will be surrounded by a path of constant width with the same area as the flower bed. Calculate the perimeter of the outside of the path.<BR>\n" );
document.write( "a) set up a quadratic equation to model the situation <BR>\n" );
document.write( "b) use the quadratic formula to solve the problem </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #664768 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=664768\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  The parks department is planning a new flower bed outside city hall.<BR>\n" );
document.write( " It will be rectangular with dimensions 9m by 6m. <BR>\n" );
document.write( " The flower bed will be surrounded by a path of constant width with the same area as the flower bed.<BR>\n" );
document.write( " Calculate the perimeter of the outside of the path.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "the area of the flower bed: 9*6 = 54 sq/m, (also the area of the path)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "a) set up a quadratic equation to model the situation<BR>\n" );
document.write( "let w = the width of the path around the flower bed<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(2w+9) by 2w+6) = the overall dimensions (garden and path)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "the overall area - flower bed area = path area<BR>\n" );
document.write( "(2w+9)*(2w+6) - 54 = 54<BR>\n" );
document.write( "FOIL<BR>\n" );
document.write( "4w^2 + 12w + 18w + 54 - 54 - 54 = 0<BR>\n" );
document.write( "A quadratic equation<BR>\n" );
document.write( "4w^2 + 30w - 54 = 0<BR>\n" );
document.write( "simplify, divide by 2<BR>\n" );
document.write( "2w^2 + 15w - 27 = 0<BR>\n" );
document.write( ":<BR>\n" );
document.write( "b) use the quadratic formula to solve the problem<BR>\n" );
document.write( "2w^2 + 15w - 27 = 0; factors to:<BR>\n" );
document.write( "(2w-3)(w+9) = 0<BR>\n" );
document.write( "The positive solution is all we want here<BR>\n" );
document.write( "2w = 3 <BR>\n" );
document.write( "w = 1.5 m is the width of the path<BR>\n" );
document.write( ":<BR>\n" );
document.write( "\"Calculate the perimeter of the outside of the path.\"<BR>\n" );
document.write( "Find the overall dimensions<BR>\n" );
document.write( "2(1.5) + 9 = 12m long<BR>\n" );
document.write( "2(1.5) + 6 = 9m wide<BR>\n" );
document.write( "P = 2(12) + 2(9)<BR>\n" );
document.write( "p = 42 meters is the perimeter<BR>\n" );
document.write( ":<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );