document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=702624>Question 702624</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The area of a right triangle is 4 . The sum of the lengths of the two sides adjacent to the right angle of the triangle is 9 . What is the length of the hypotenuse of the triangle? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #433072 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39630)</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=433072\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Right triangle shown below, hypotenuse unlabeled, and legs x and y lengths.<BR>\n" );
document.write( "Area was given as 4 [square units]:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%2Ax%2Ay=4 ALIGN=MIDDLE  ALT=\"%281%2F2%29%2Ax%2Ay=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The sum of the legs' lengths given as 9 units:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=9 ALIGN=MIDDLE  ALT=\"x%2By=9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now we have two equations and two unknowns, x and y.  <BR>\n" );
document.write( "From the area equation, we obtain <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=8%2Fy ALIGN=MIDDLE  ALT=\"x=8%2Fy\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which we directly substitute into the length equation to obtain <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288%2Fy%29%2By=9 ALIGN=MIDDLE  ALT=\"%288%2Fy%29%2By=9\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Clearing the fraction yields <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2-9%2Ay%2B8=0 ALIGN=MIDDLE  ALT=\"y%5E2-9%2Ay%2B8=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "...General solution to quadratic formula will give y = 1 or 8.  This is just fine.  Checking each using either equation from our system, gives x = 8 or 1.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "ANSWER: The length of the legs are 1 and 8.<BR>\n" );
document.write( "(please scroll down to see picture.)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+300%2C+320%2C+0%2C+10%2C+0%2C+10%2C%0D%0A++++++++++++line%28+1%2C1%2C9%2C1%29%2C%0D%0A++++++++++++line%28+9%2C1%2C9%2C2%29%2C%0D%0A++++++++++++line%28+9%2C2%2C1%2C1%29%2C%0D%0A++++++++++++locate%285%2C0.5%2CX%29%2C%0D%0A++++++++++++locate%289.5%2C1.5%2CY%29+%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );