document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=564768>Question 564768</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Lee has a rectangular plot to use for a flower garden. She plans to include a gravel<BR>\n" );
document.write( "border of uniform width around the flower garden so visitors can walk completely around<BR>\n" );
document.write( "the flowers to view them more easily. The total size of the garden and gravel border is to<BR>\n" );
document.write( "be 15 feet by 21 feet. If Lee has enough gravel to cover 117 square feet for the border,<BR>\n" );
document.write( "how wide will the gravel border be? What will the dimensions of the actual flower garden<BR>\n" );
document.write( "be? Round answers to nearest tenth. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #365498 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=365498\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let x = the width of the border.<BR>\n" );
document.write( "the total area including the border is equal to 315 square feet.<BR>\n" );
document.write( "the area of the border is equal to 117 square feet.<BR>\n" );
document.write( "subtract 117 from 315 and you get 198 square feet for the garden.<BR>\n" );
document.write( "the length of the garden will be equal to 21 - 2x.<BR>\n" );
document.write( "the width of the garden will be equal to 15 - 2x.<BR>\n" );
document.write( "since the area of the garden is equal to the length times the width, then the equation for the area of the garden will be:<BR>\n" );
document.write( "(21 - 2x) * (15 - 2x) = 198 square feet.<BR>\n" );
document.write( "we multiply these factors out to get:<BR>\n" );
document.write( "4x^2 - 72x + 315 = 198<BR>\n" );
document.write( "we subtract 198 from both sides of this equation to get:<BR>\n" );
document.write( "4x^2 - 72x + 117 = 0<BR>\n" );
document.write( "this doesn't factor well so we use the quadratic formula to get:<BR>\n" );
document.write( "x = 16.19374728 or x = 1.806252715<BR>\n" );
document.write( "x = 16.19374728 doesn't work because 21 - 2*16 is negative.<BR>\n" );
document.write( "the answer has to be x = 1.806252715 or there is no solution.<BR>\n" );
document.write( "we go back to our equation for the area of the garden.<BR>\n" );
document.write( "it is:<BR>\n" );
document.write( "(21 - 2x) * (15 - 2x) = 198 square feet.<BR>\n" );
document.write( "substituting 1.806252715 for x gets us:<BR>\n" );
document.write( "21 - 2*1.806252715) * (15 - 2*1.806252715) = 198<BR>\n" );
document.write( "simplifying this equation gets us:<BR>\n" );
document.write( "17.38749457 * 11.38749457 = 198<BR>\n" );
document.write( "simplifying this further gets:<BR>\n" );
document.write( "198 = 198.<BR>\n" );
document.write( "this confirms the value for x is good.<BR>\n" );
document.write( "we confirm even further by determining the area of the border.<BR>\n" );
document.write( "that will be:<BR>\n" );
document.write( "4 * x^2 plus 2 *(21 - 2x) * x plus 2 * (15-2x) * x<BR>\n" );
document.write( "substituting for x in this equation gets us 117 square feet.<BR>\n" );
document.write( "the area of the garden is 198 square feet.<BR>\n" );
document.write( "the area of the border is 117 square feet.<BR>\n" );
document.write( "the value of x = 1.806252715 feet.<BR>\n" );
document.write( "x is the width of the border.<BR>\n" );
document.write( "the length of the garden will be 21 - 2x = = 17.38749457<BR>\n" );
document.write( "the width of the garden will be 15 - 2x = 11.38749457<BR>\n" );
document.write( "the area of the garden is equal to (21-2x) * (15-2x) = 198 square feet.<BR>\n" );
document.write( "the equation we solved using the quadratic formula is:<BR>\n" );
document.write( "4x^2 - 72x + 117 = 0<BR>\n" );
document.write( "in that equation:<BR>\n" );
document.write( "a = 4<BR>\n" );
document.write( "b = -72<BR>\n" );
document.write( "c = 117<BR>\n" );
document.write( "the quadratic formula is:<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-b+%2B-+sqrt%28b%5E2-4ac%29%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"%28-b+%2B-+sqrt%28b%5E2-4ac%29%29%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "your answer need to be to the nearest tenth of a foot.<BR>\n" );
document.write( "that makes your answer:<BR>\n" );
document.write( "the width of the border is equal to 1.8 feet.<BR>\n" );
document.write( "the length of the garden is equal to 17.4 feet<BR>\n" );
document.write( "the width of the garden is equal to 11.4 feet.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );