document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=329728>Question 329728</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1) the lengths of the three sides of a rigt angled triangle are x-2, 2x, and x+6. x+6 is the longest side of the triangle. what is the length of the shortest side of the triangle?\r<BR>\n" );
document.write( "\n" );
document.write( "2) th diference betwen two positive number is 3. the difference between their reciprocals is 1/90. what are the two numbers? (Note: the reciprocal of x is 1/x) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #236418 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=236418\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1) the lengths of the three sides of a rigt angled triangle are x-2, 2x, and x+6. x+6 is the longest side of the triangle. what is the length of the shortest side of the triangle?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B6%29%5E2+=+%28x-2%29%5E2+%2B+%282x%29%5E2 ALIGN=MIDDLE  ALT=\"%28x%2B6%29%5E2+=+%28x-2%29%5E2+%2B+%282x%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=x%5E2+%2B+12x+%2B+36+=+x%5E2+-+4x+%2B+4+%2B+4x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+12x+%2B+36+=+x%5E2+-+4x+%2B+4+%2B+4x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2+-16x+-32+=+0 ALIGN=MIDDLE  ALT=\"4x%5E2+-16x+-32+=+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+-+4x+-+8+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+-+4x+-+8+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = 2 ± 4sqrt(3)<BR>\n" );
document.write( "x-2 = +4sqrt(3) the shortest side<BR>\n" );
document.write( "------------------<BR>\n" );
document.write( "2) th diference betwen two positive number is 3. the difference between their reciprocals is 1/90. what are the two numbers? (Note: the reciprocal of x is 1/x)<BR>\n" );
document.write( "----------<BR>\n" );
document.write( "Thx for the info on reciprocals.<BR>\n" );
document.write( "x is the larger number.<BR>\n" );
document.write( "x - y = 3<BR>\n" );
document.write( "1/x - 1/y = -1/90 (minus because the recip of a larger # is smaller)<BR>\n" );
document.write( "Multiply by 90xy<BR>\n" );
document.write( "90y - 90x = -xy<BR>\n" );
document.write( "x = y+3, sub for x<BR>\n" );
document.write( "------------<BR>\n" );
document.write( "90y - 90*(y+3) = -y*(y+3) = -y^2 - 3y<BR>\n" );
document.write( "y^2 + 3y = 270<BR>\n" );
document.write( "y^2 + 3y - 270 = 0<BR>\n" );
document.write( "(y + 18)*(y - 15) = 0<BR>\n" );
document.write( "y = 15<BR>\n" );
document.write( "x = 18<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );