document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=996106>Question 996106</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A landowner wishes to use 3 miles of fencing to enclose an isosceles triangular region of as large an area as possible. What should be the lengths of the sides of the triangle?\r<BR>\n" );
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document.write( "Let x be the length of the base of the triangle. Write the area as a function of x. [First write the length of the equal-length sides in terms of the base, x, then write the height of the triangle in terms of the base.] \r<BR>\n" );
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document.write( "A(x) =  <BR>\n" );
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document.write( "Length of base = ? miles<BR>\n" );
document.write( "Length of the other two (equal-length) sides =  ? miles each\r<BR>\n" );
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document.write( "Thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #614675 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39621)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=614675\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Done part-way through but not including the derivative & maximization work:\r<BR>\n" );
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document.write( "Draw a triangle, base x, height h, the two equal sides each d.  Cut x exactly in half forming two of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F2 ALIGN=MIDDLE  ALT=\"x%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "The drawing allows you to first form two equations.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%282d%2Bx=3%2C%28x%2F2%29%5E2%2Bh%5E2=d%5E2%29 ALIGN=MIDDLE  ALT=\"system%282d%2Bx=3%2C%28x%2F2%29%5E2%2Bh%5E2=d%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Starting with perimeter equation solve for d in terms of x.<BR>\n" );
document.write( "This part will be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=%281%2F2%29%283-x%29 ALIGN=MIDDLE  ALT=\"d=%281%2F2%29%283-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Substitute this formula for d into the pythagorean relation ship equation and solve for h:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2F2%29%5E2%2Bh%5E2=%28%281%2F2%29%283-x%29%29%5E2 ALIGN=MIDDLE  ALT=\"%28x%2F2%29%5E2%2Bh%5E2=%28%281%2F2%29%283-x%29%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5E2=%281%2F2%29%5E2%2A%283-x%29%5E2-%28x%2F2%29%5E2 ALIGN=MIDDLE  ALT=\"h%5E2=%281%2F2%29%5E2%2A%283-x%29%5E2-%28x%2F2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5E2=%281%2F4%29%28%283-x%29%5E2-x%5E2%29 ALIGN=MIDDLE  ALT=\"h%5E2=%281%2F4%29%28%283-x%29%5E2-x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=%281%2F2%29sqrt%289-6x%2Bx%5E2-x%5E2%29 ALIGN=MIDDLE  ALT=\"h=%281%2F2%29sqrt%289-6x%2Bx%5E2-x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28h=%281%2F2%29sqrt%289-6x%29%29 ALIGN=MIDDLE  ALT=\"highlight_green%28h=%281%2F2%29sqrt%289-6x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "A(x) will be the area function.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%28x%29=%281%2F2%29x%2Ah ALIGN=MIDDLE  ALT=\"A%28x%29=%281%2F2%29x%2Ah\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and now you have a formula for h.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28A%28x%29=%281%2F2%29x%2Asqrt%289-6x%29%29 ALIGN=MIDDLE  ALT=\"highlight_green%28A%28x%29=%281%2F2%29x%2Asqrt%289-6x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Omitting the differentiation steps but starting with the product rule, I am finding <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dA%2Fdx=%289-9x%29%2F%284sqrt%289-6x%29%29 ALIGN=MIDDLE  ALT=\"dA%2Fdx=%289-9x%29%2F%284sqrt%289-6x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >; and you can continue the maximization process... </SPAN>\n" );
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