document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=271986>Question 271986</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can someone please help me with this word problem:\r<BR>\n" );
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document.write( "The area of a rectangle with the perimeter 100 in. is given by the formula:  A=50w-w^2 where w is the width.  Find the value of w that produces the maximum area.  \r<BR>\n" );
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document.write( "the only way i could try to figure this out is to make columns with the length and width dimensions that equal 100 in perimeter and plug the width into the equation.  I started using the width of 45 and worked down to 30 which has the area of 600.  But since a square is also a rectangle, do I use 25?  Is there an easier way to figure this?  Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #199055 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=199055\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Yes, there is an easier way using algebra.<BR>\n" );
document.write( "Graph the given function which that shows the area (A) as a function of the width (w). A (area) is the vertical axis while w (width) is the horizontal axis.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-5%2C60%2C-5%2C660%2C50x-x%5E2%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-5%2C60%2C-5%2C660%2C50x-x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You can see from the graph that this is a parabola opening downward so there is a maximum (area) at (w, A) of (25, 625).<BR>\n" );
document.write( "You can find the w coordinate of the vertex by:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w+=+%28-b%29%2F2a ALIGN=MIDDLE  ALT=\"w+=+%28-b%29%2F2a\"   DISABLED_style= \"max-width:90%; height:auto;\" > where: b = 50 and a = -1, so...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w+=+%28-50%29%2F%282%28-1%29%29 ALIGN=MIDDLE  ALT=\"w+=+%28-50%29%2F%282%28-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w+=+25 ALIGN=MIDDLE  ALT=\"w+=+25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The vertex (maximum area in this case) occurs at w = 25.  </SPAN>\n" );
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