document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=894103>Question 894103</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi I would like a calculus answer to this problem (Using a derivative)\r<BR>\n" );
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document.write( "What is the maximum area of a right angled triangle with perimeter 72?\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 #541757 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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/cgi-bin/show-face.mpl?user=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=541757\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Form a right triangle, sides A and B, hypotenuse C.<BR>\n" );
document.write( "Perimeter:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%2BB%2BC=72 ALIGN=MIDDLE  ALT=\"A%2BB%2BC=72\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Pythagorean theorem:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5E2%2BB%5E2=C%5E2 ALIGN=MIDDLE  ALT=\"A%5E2%2BB%5E2=C%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Let's get rid of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C ALIGN=MIDDLE  ALT=\"C\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=72-A-B ALIGN=MIDDLE  ALT=\"C=72-A-B\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5E2=%2872-A-B%29%5E2 ALIGN=MIDDLE  ALT=\"C%5E2=%2872-A-B%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5E2%2BB%5E2=A%5E2%2B2AB-144A%2BB%5E2-144B%2B5184 ALIGN=MIDDLE  ALT=\"A%5E2%2BB%5E2=A%5E2%2B2AB-144A%2BB%5E2-144B%2B5184\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=2AB-144A-144B%2B5184 ALIGN=MIDDLE  ALT=\"0=2AB-144A-144B%2B5184\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B%282A-144%29=144A-5184 ALIGN=MIDDLE  ALT=\"B%282A-144%29=144A-5184\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=%28144A-5184%29%2F%282A-144%29 ALIGN=MIDDLE  ALT=\"B=%28144A-5184%29%2F%282A-144%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=%2872%28A-36%29%29%2F%28A-72%29 ALIGN=MIDDLE  ALT=\"B=%2872%28A-36%29%29%2F%28A-72%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Area (Use Y instead of A):<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y=%281%2F2%29AB ALIGN=MIDDLE  ALT=\"Y=%281%2F2%29AB\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Maximize the area. <BR>\n" );
document.write( "Make Y a function of only 1 variable.<BR>\n" );
document.write( "Substitute,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y=%281%2F2%29A%2A%28%2872%28A-36%29%29%2F%28A-72%29%29 ALIGN=MIDDLE  ALT=\"Y=%281%2F2%29A%2A%28%2872%28A-36%29%29%2F%28A-72%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=Y=%2836A%5E2-1296A%29%2F%28A-72%29 ALIGN=MIDDLE  ALT=\"Y=%2836A%5E2-1296A%29%2F%28A-72%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Take the derivative using the quotient rule,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dY%2Fdx=%28%28A-72%29%2872A-1296%29-%2836A%5E2-1296A%29%281%29%29%2F%28A-72%29%5E2 ALIGN=MIDDLE  ALT=\"dY%2Fdx=%28%28A-72%29%2872A-1296%29-%2836A%5E2-1296A%29%281%29%29%2F%28A-72%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=dY%2Fdx=%2836%28A%5E2-144A%2B2592%29%29%2F%28A-72%29%5E2 ALIGN=MIDDLE  ALT=\"dY%2Fdx=%2836%28A%5E2-144A%2B2592%29%29%2F%28A-72%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now set it equal to zero.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5E2-144A%2B2592=0 ALIGN=MIDDLE  ALT=\"A%5E2-144A%2B2592=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5E2-144A%2B5184%2B2592=5184 ALIGN=MIDDLE  ALT=\"A%5E2-144A%2B5184%2B2592=5184\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28A-72%29%5E2=5184-2592 ALIGN=MIDDLE  ALT=\"%28A-72%29%5E2=5184-2592\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28A-72%29%5E2=2592 ALIGN=MIDDLE  ALT=\"%28A-72%29%5E2=2592\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A-72=0+%2B-+36sqrt%282%29 ALIGN=MIDDLE  ALT=\"A-72=0+%2B-+36sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=72+%2B-+36sqrt%282%29 ALIGN=MIDDLE  ALT=\"A=72+%2B-+36sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A ALIGN=MIDDLE  ALT=\"A\"   DISABLED_style= \"max-width:90%; height:auto;\" > cannot be greater than 72, <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=72-36sqrt%282%29 ALIGN=MIDDLE  ALT=\"A=72-36sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=%2872%28A-36%29%29%2F%28A-72%29 ALIGN=MIDDLE  ALT=\"B=%2872%28A-36%29%29%2F%28A-72%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=%2872%2836-36sqrt%282%29%29%29%2F%28-36sqrt%282%29%29 ALIGN=MIDDLE  ALT=\"B=%2872%2836-36sqrt%282%29%29%29%2F%28-36sqrt%282%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=B=72-36sqrt%282%29 ALIGN=MIDDLE  ALT=\"B=72-36sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "It's an isosceles right triangle.<BR>\n" );
document.write( "So then,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y=%281%2F2%29%28AB%29 ALIGN=MIDDLE  ALT=\"Y=%281%2F2%29%28AB%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y=%281%2F2%29%2872-36sqrt%282%29%29%5E2 ALIGN=MIDDLE  ALT=\"Y=%281%2F2%29%2872-36sqrt%282%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=Y=%281%2F2%29%285184-2592sqrt%282%29-2592sqrt%282%29%2B2592%29 ALIGN=MIDDLE  ALT=\"Y=%281%2F2%29%285184-2592sqrt%282%29-2592sqrt%282%29%2B2592%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y=%281%2F2%29%287776-5184sqrt%282%29%29 ALIGN=MIDDLE  ALT=\"Y=%281%2F2%29%287776-5184sqrt%282%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=highlight%28Y=3888-2592sqrt%282%29%29 ALIGN=MIDDLE  ALT=\"highlight%28Y=3888-2592sqrt%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );