document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=969740>Question 969740</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Jack would like to erect a fence on all four sides of his new garden with an area of 225m^2. The fencing will cost him $35 per metre. In order to use the least fencing he would like the garden to be a minimum. The fence will be supported by wooden fence poles, approximately 1.5 m apart and a gate 1.5 m long, made of the same fence can be placed between any two poles. Each wooden fence pole would cost $9.50\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1. Calculate the lenght of each side of the garden\r<BR>\n" );
document.write( "\n" );
document.write( "2.How many metres of fencing will he need?\r<BR>\n" );
document.write( "\n" );
document.write( "3. How many fence poles will he need?\r<BR>\n" );
document.write( "\n" );
document.write( "4. How much will the fencing and the fence poles, excluding the gate, cost him?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(Please I really need help) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #592519 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=592519\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A square is the rectangle that minimizes the perimeter for a given area.  Here is why without proving (first).  If a rectangle has area 225 m^2, 15^2 (perimeter 4*15m=60m) is the best.  For 25*9=225 , the perimeter is 68.  For 45 *5=225, The perimeter is 100.  The proof is much easier with calculus, but here is how I would go about it.\r<BR>\n" );
document.write( "\n" );
document.write( "Let x and y be the length and the width, respectively.<BR>\n" );
document.write( "Then 2x + 2y =perimeter; the area is xy\r<BR>\n" );
document.write( "\n" );
document.write( "2x= perimeter-2y<BR>\n" );
document.write( "xy,  or the area,  now become (perimeter-2y) y  =perimeter*y-2y^2<BR>\n" );
document.write( "This is a parabola, with the vertex at -b/2a  or   -(perimeter)/-2 or half of the perimeter.  <BR>\n" );
document.write( "So y in the area formula is half the perimeter.  That means x has to be half the perimeter as well.<BR>\n" );
document.write( "I don't see the gate as adding or subtracting from the 60 m perimeter.\r<BR>\n" );
document.write( "\n" );
document.write( "There are 4 corner poles.  There are 9 poles between each corner, which would be 36 poles in between..\r<BR>\n" );
document.write( "\n" );
document.write( "x=y  and x^2=225 m^2, so x and y are both 15 m.  \r<BR>\n" );
document.write( "\n" );
document.write( "The length of each side is 15 m\r<BR>\n" );
document.write( "\n" );
document.write( "Fencing needed = 60 m.  (including 1.5 m  for the gate.  I think that needs to be mentioned)\r<BR>\n" );
document.write( "\n" );
document.write( "Fencing poles needed=40\r<BR>\n" );
document.write( "\n" );
document.write( "Cost is 60*35 for fencing=$2100.  60 meters *$35/meter.<BR>\n" );
document.write( "Cost of poles is 40*$9.50=$380<BR>\n" );
document.write( "I get $2480 MINUS the cost of the fence, which is $35*1.5 meters or $52.50<BR>\n" );
document.write( "Cost now is $2422.50.\r<BR>\n" );
document.write( "\n" );
document.write( "I am hoping there are no tricks with the poles and the gate.  \r<BR>\n" );
document.write( "\n" );
document.write( "By the way, the maximum product for a given pair of numbers with a constant sum is when the numbers are the same.  It is sort of the same idea.  For a given amount of fence, you maximize the area it encloses when you make it a square.  Here, you have a given area, so you are looking at minimizing the amount of fence.    \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );