document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=102929>Question 102929</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Pls help me with this. It's really hard!!<BR>\n" );
document.write( "A farmer wants to make a rectangular garden of 7500 square meters, and she has 250 meters of fencing material. There is already a fence on one side. What dimensions should her garden have?<BR>\n" );
document.write( "I really need some explanation here. Pls help me. thanks.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #74854 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=74854\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let L represent the length of the rectangle and W represent the width of the rectangle.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "The area of the rectangle is to be 7500 square meters.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "The area of a rectangle equals the product of the length L and the width W or:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "A = L * W<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Now substitute 7500 for the area to change the equation to:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "7500 = L * W<BR>\n" );
document.write( ".<BR>\n" );
document.write( "The 250 meters of fencing is a little tricky. This fencing will only be needed on 3 sides of<BR>\n" );
document.write( "the rectangle because the 4th side is an existing fence.  So we can say that the fencing material<BR>\n" );
document.write( "will be used for the Length and the two Widths to be installed, and the existing fence will<BR>\n" );
document.write( "be used for the other Length. So the 250 meters of fence will equal L plus 2W. In equation<BR>\n" );
document.write( "form this is:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "250 = L + 2W<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Now return to the area equation. We can solve it for W by dividing both sides by L to get:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "W = 7500/L<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Substitute the right side of this for W in the fence length equation to get:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "250 = L + 2W = L + 2(7500/L) = L + 15000/L<BR>\n" );
document.write( ".<BR>\n" );
document.write( "So start with <BR>\n" );
document.write( ".<BR>\n" );
document.write( "250 = L + 15000/L<BR>\n" );
document.write( ".<BR>\n" );
document.write( "You can get rid of the denominator by multiplying both sides of this equation (all terms)<BR>\n" );
document.write( "by L to make the equation become:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "250L = L^2 + 15000<BR>\n" );
document.write( ".<BR>\n" );
document.write( "To get this in \"standard form\" for solving, make the left side equal zero by subtracting<BR>\n" );
document.write( "250L from both sides to change the equation to:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "0 = L^2 - 250L + 15000<BR>\n" );
document.write( ".<BR>\n" );
document.write( "A little more standard form is obtained by simply transposing sides to get:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "L^2 - 250L + 15000 = 0<BR>\n" );
document.write( ".<BR>\n" );
document.write( "The left side of this equation can be factored to:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "(L - 150)(L - 100) = 0<BR>\n" );
document.write( ".<BR>\n" );
document.write( "This equation will be true if either of the factors equals zero ... because a multiplication<BR>\n" );
document.write( "by zero on the left side will make the left side of the equation equal the zero on the <BR>\n" );
document.write( "right side.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Setting each factor equal to zero means:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "L - 150 = 0 or L = 150 <BR>\n" );
document.write( ".<BR>\n" );
document.write( "and L - 100 = 0 or L = 100<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Let's first choose L = 150 meters.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "That leaves 100 meters of fencing material (250 meters - 150 meters) to use in making the<BR>\n" );
document.write( "2 widths. So each of the widtha is 100 meters divided by 2 or 50 meters.  <BR>\n" );
document.write( ".<BR>\n" );
document.write( "So this solution is to make the rectangle 150 meters by 50 meters which multiplies out<BR>\n" );
document.write( "to give an area of 7500 square meters and use the 250 meters of fence as 2 widths of<BR>\n" );
document.write( "50 meters each and a length of 150 meters. 150 meters of the existing fence is used for<BR>\n" );
document.write( "the 4th side<BR>\n" );
document.write( ".<BR>\n" );
document.write( "How about our other potential solution of L = 100 meters? That means that if you cut 100 meters<BR>\n" );
document.write( "of fence for the length, you have 150 meters left over for the 2 widths. So each width <BR>\n" );
document.write( "is 75 meters. This makes the dimensions of the garden 100 by 75 meters. This means that<BR>\n" );
document.write( "the area is 100 times 75 which is 7500 square meters. And the 100 meters plus 75 meters plus<BR>\n" );
document.write( "75 meters for the sides adds up to the 250 meters of fencing. The existing fencing can<BR>\n" );
document.write( "supply the missing 100 meter length.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "So there are two answers to this problem. One is to make the rectangle 50 by 150 meters,<BR>\n" );
document.write( "using the existing fence to provide one of the 150 meter sides. The other is to make <BR>\n" );
document.write( "the rectangle 75 by 100 meters, using the existing fence to provide one of the 100 meter<BR>\n" );
document.write( "sides. <BR>\n" );
document.write( ".<BR>\n" );
document.write( "Hope this helps you to understand the problem. <BR>\n" );
document.write( ".<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );