document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=515755>Question 515755</A>: <I><SPAN STYLE=\"word-break: break-all;\"> what must be the value of x and y if the area is to be a minimum and the perimeter is to be 300m? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #344158 by </B><A HREF=/tutors/aboutme.mpl?userid=oberobic><B>oberobic(2304)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=oberobic><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=344158\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x = length<BR>\n" );
document.write( "y = width<BR>\n" );
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document.write( "To maximize the area, use a square.  To minimize the area, decrease x and increase y by the same amount.<BR>\n" );
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document.write( "The perimeter = 300 (a constant)<BR>\n" );
document.write( "2(x+y) = 300<BR>\n" );
document.write( "x+y = 150<BR>\n" );
document.write( "x = 150-y<BR>\n" );
document.write( "y = 150-x<BR>\n" );
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document.write( "Area of a square = 75^2 = 5625 m^2 = maximum<BR>\n" );
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document.write( "To find the minimum area...<BR>\n" );
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document.write( "Assume the rectangle is 1x149.  <BR>\n" );
document.write( "Perimeter = 2(1+149) = 2(150) = 300 m.<BR>\n" );
document.write( "Area = 1*149 = 149 m^2<BR>\n" );
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document.write( "Assuming 'x' can be made infinitely small, then it can practically disappear.<BR>\n" );
document.write( "As 'x' gets closer and closer to 0, the 'y' gets closer and closer to 150 m.<BR>\n" );
document.write( "Recall y = 150-x.<BR>\n" );
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document.write( "Assume 'x' is 1 cm = .01 m. Then 'y' will be 150-.01 = 149.99 m.<BR>\n" );
document.write( ".01*149.99 =  1.4999 m^2<BR>\n" );
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document.write( "Assume 'x' is 1 mm = .001 m. Then 'y' will be 150-.001 = 149.999<BR>\n" );
document.write( "Area = .001*149.999 = .149999 m^2<BR>\n" );
document.write( "etc.<BR>\n" );
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document.write( "As you may have guessed. the limit of the area as 'x' approaches 0 is 0 m^2.  That would the case where the fence was doubled back on itself with no area at all.  The perimeter would still be 300, though it would look like a fence line 150 m long that was double thickness.<BR>\n" );
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