document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1002047>Question 1002047</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of the lengths of the two perpendicular sides of a right triangle is 30 centimeters. What are their lengths if the square of the hypotenuse is a minimum? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #619063 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</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=619063\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> h, hypotenuse<BR>\n" );
document.write( "x and 30-x are lengths of the legs.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5E2=x%5E2%2B%2830-x%29%5E2 ALIGN=MIDDLE  ALT=\"h%5E2=x%5E2%2B%2830-x%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=x%5E2%2B30%5E2-60x%2Bx%5E2 ALIGN=MIDDLE  ALT=\"h%5E2=x%5E2%2B30%5E2-60x%2Bx%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=2x%5E2-60x%2B900 ALIGN=MIDDLE  ALT=\"h%5E2=2x%5E2-60x%2B900\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Find the x value or values for the minimum <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5E2 ALIGN=MIDDLE  ALT=\"h%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2-60x%2B900=0 ALIGN=MIDDLE  ALT=\"2x%5E2-60x%2B900=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-30x%2B450=0 ALIGN=MIDDLE  ALT=\"x%5E2-30x%2B450=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Discriminant, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=900-4%2A450=NegativeNumber ALIGN=MIDDLE  ALT=\"900-4%2A450=NegativeNumber\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This method, finding the roots, will not work here because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5E2 ALIGN=MIDDLE  ALT=\"h%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > as a function does not intersect the x-axis.\r<BR>\n" );
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document.write( "You can complete the square for making into standard form, and then read the vertex  (a minimum point) from that form of the equation.  The term to use is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2830%2F2%29%5E2=15%5E2 ALIGN=MIDDLE  ALT=\"%2830%2F2%29%5E2=15%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or 225.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-30x%2B15%5E2%2B450-225=0 ALIGN=MIDDLE  ALT=\"x%5E2-30x%2B15%5E2%2B450-225=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-15%29%5E2%2B225=0 ALIGN=MIDDLE  ALT=\"%28x-15%29%5E2%2B225=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Showing x=15 for the vertex, and then one leg of the triangle is 15, and therefore the other leg is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30-x=30-15=15 ALIGN=MIDDLE  ALT=\"30-x=30-15=15\"   DISABLED_style= \"max-width:90%; height:auto;\" > also. </SPAN>\n" );
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