document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=967811>Question 967811</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The hypotenuse of a right angled triangle exceeds one side by 1cm and the other side by 18cm,Calculate the length of the shortest side? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #591543 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52781)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=591543\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
document.write( "\n" );
document.write( "Let &nbsp;x&nbsp; be the length of the hypotenuse of the given right angled triangle.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Then the length of one leg is &nbsp;x-1, &nbsp;and the length of the other leg is &nbsp;x-18, &nbsp;according to the condition.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Then the Pythagorean theorems gives an equation\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%29%5E2 ALIGN=MIDDLE  ALT=\"%28x-1%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > +  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-18%29%5E2 ALIGN=MIDDLE  ALT=\"%28x-18%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Simplify and solve it step by step to find &nbsp;x.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+2x+%2B+1 ALIGN=MIDDLE  ALT=\"x%5E2+-+2x+%2B+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+36x+%2B+324 ALIGN=MIDDLE  ALT=\"x%5E2+-+36x+%2B+324\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >,\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+38x+%2B+325 ALIGN=MIDDLE  ALT=\"x%5E2+-+38x+%2B+325\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D ALIGN=MIDDLE  ALT=\"x%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2838+%2B+sqrt%2838%5E2+-+4%2A325%29%29%2F2 ALIGN=MIDDLE  ALT=\"%2838+%2B+sqrt%2838%5E2+-+4%2A325%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2838+%2B+sqrt%28144%29%29%2F2 ALIGN=MIDDLE  ALT=\"%2838+%2B+sqrt%28144%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2838+%2B+12%29%2F2 ALIGN=MIDDLE  ALT=\"%2838+%2B+12%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25 ALIGN=MIDDLE  ALT=\"25\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D ALIGN=MIDDLE  ALT=\"x%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2838+-+sqrt%2838%5E2+-+4%2A325%29%29%2F2 ALIGN=MIDDLE  ALT=\"%2838+-+sqrt%2838%5E2+-+4%2A325%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2838+-+sqrt%28144%29%29%2F2 ALIGN=MIDDLE  ALT=\"%2838+-+sqrt%28144%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2838+-+12%29%2F2 ALIGN=MIDDLE  ALT=\"%2838+-+12%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13 ALIGN=MIDDLE  ALT=\"13\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Thus there are two solutions for the hypotenuse: &nbsp;25 units and/or &nbsp;13 units. &nbsp;Since one leg is 18 units shorter than the hypotenuse, &nbsp;only one solution has sense: &nbsp;x = 25.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<B>Answer</B>.&nbsp; The hypotenuse is 25 units long. &nbsp;The legs are of 24  and 7 units long. &nbsp;The shortest side is of &nbsp;7 units long.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );