document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=86386>Question 86386</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Alan is building a garden shaped like a rectangle with a semicircle attached to one short side.  If he has 70 feet of fencing to go around it, what dimensions will give him the maximum area in the garden?\r<BR>\n" );
document.write( "\n" );
document.write( "I know that eventually you may have to use the X=b/2a formula<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 #62504 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=62504\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Alan is building a garden shaped like a rectangle with a semicircle attached to one short side.  If he has 70 feet of fencing to go around it, what dimensions will give him the maximum area in the garden?<BR>\n" );
document.write( "----------------<BR>\n" );
document.write( "Draw the picture.<BR>\n" );
document.write( "Let the shorter side be \"x\"<BR>\n" );
document.write( "Perimeter of the semi-circle is (pi)x<BR>\n" );
document.write( "Twice the Length of the longer side is [70-(pi)x -x]<BR>\n" );
document.write( "Length = [70-(1+pi)x]/2 <BR>\n" );
document.write( "Total area = area of rectangle + area of the semi-circle.<BR>\n" );
document.write( "Total area = x[[70-(1+pi)x]/2] + [(pi)(x/2)^2]/2<BR>\n" );
document.write( "2Total area = 70x -(1+pi)x^2 +  [(pi)(x^2/4)]<BR>\n" );
document.write( "2Total area = 70x +[(pi/4)-(1+pi)]x^2<BR>\n" );
document.write( "2Total area = 70x - [3.3562]x^2<BR>\n" );
document.write( "Total area = 35x - 1.6781x^2<BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "Max occurs at x = 35/2*1.6781= 20.8569(shorter side)<BR>\n" );
document.write( "Longer side = [70-(1+pi)*10.4285]/2 = 13.4047 (longer side)<BR>\n" );
document.write( "================<BR>\n" );
document.write( "Comment: The method here is correct; the arithmetic may be less<BR>\n" );
document.write( "than the accuracy you require.  I recommend you check it out.<BR>\n" );
document.write( "---------<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );