document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1043677>Question 1043677</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the dimensions and area of the largest rectangle that can be inscribed in a right angle triangle, whose sides have lengths of 9cm, 12cm and a hypotenuse of 15cm. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #659021 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=659021\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  Find the dimensions and area of the largest rectangle that can be inscribed in a right angle triangle, whose sides have lengths of 9cm, 12cm and a hypotenuse of 15cm. <BR>\n" );
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document.write( "let x = the width of the rectangle<BR>\n" );
document.write( "let y = the length<BR>\n" );
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document.write( "Draw out a right triangle with the rectangle inscribed therein, x by y <BR>\n" );
document.write( "the height of the right triangle = 12 and the base = 9<BR>\n" );
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document.write( "We are interested in the small right triangles adjacent the inscribed rectangle<BR>\n" );
document.write( "The tangent of the top angle = 9/12 which = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F%28%2812-y%29%29 ALIGN=MIDDLE  ALT=\"x%2F%28%2812-y%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the small right triangle on top<BR>\n" );
document.write( "Cross multiply<BR>\n" );
document.write( "12x = 9(12-y)<BR>\n" );
document.write( "12x = 108 - 9y<BR>\n" );
document.write( "x = 9 - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2F12 ALIGN=MIDDLE  ALT=\"9%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" >y<BR>\n" );
document.write( "similarly, the tangent of the base angle = 12/9 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2F%28%289-x%29%29 ALIGN=MIDDLE  ALT=\"y%2F%28%289-x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Cross multiply<BR>\n" );
document.write( "9y = 12(9-x)<BR>\n" );
document.write( "9y = 108 - 12x<BR>\n" );
document.write( "y = 12 - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2F9 ALIGN=MIDDLE  ALT=\"12%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" >x<BR>\n" );
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document.write( "Area = xy<BR>\n" );
document.write( "replace y with (12-<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2F9 ALIGN=MIDDLE  ALT=\"12%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" >x)<BR>\n" );
document.write( "A = x(12-<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2F9 ALIGN=MIDDLE  ALT=\"12%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" >x)<BR>\n" );
document.write( "A = 12x - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2F9 ALIGN=MIDDLE  ALT=\"12%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" >x^2<BR>\n" );
document.write( "A quadratic equation, max occurs at the axis of symmetry; x=-b/(2a)<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-12%29%2F%282%28-12%2F9%29%29 ALIGN=MIDDLE  ALT=\"%28-12%29%2F%282%28-12%2F9%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-12%29%2F%28-24%2F9%29 ALIGN=MIDDLE  ALT=\"%28-12%29%2F%28-24%2F9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = +4.5 cm is the width of the rectangle with max area<BR>\n" );
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document.write( "Find y<BR>\n" );
document.write( "y = 12 - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2F9 ALIGN=MIDDLE  ALT=\"12%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" >*4.5<BR>\n" );
document.write( "y = 12 - 6<BR>\n" );
document.write( "y = 6 cm is length<BR>\n" );
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document.write( "Max area: 6 * 4.5 = 27 sq/cm<BR>\n" );
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document.write( "NOt sure if I explained this clearly, let me know. CK </SPAN>\n" );
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