document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=154288>Question 154288</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The hypotenuse equals 23 units, find the size of the other two legs of a right triangle with one leg 3 units more than the other.  What is the formula? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #113599 by </B><A HREF=/tutors/aboutme.mpl?userid=orca><B>orca(409)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=orca><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=113599\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x be the length of the shorter leg, then that of the longer one is x + 3.<BR>\n" );
document.write( "Applying the Pythagorean Theorem, we have<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+%28x%2B3%29%5E2=23%5E2 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+%28x%2B3%29%5E2=23%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Solving for x, we have<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2Bx%5E2%2B6x%2B9=529 ALIGN=MIDDLE  ALT=\"x%5E2%2Bx%5E2%2B6x%2B9=529\"   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%2B6x-520=0 ALIGN=MIDDLE  ALT=\"2x%5E2%2B6x-520=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%2B3x-260=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B3x-260=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >   (divide both sides by 2)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >    (plug in a=1,b=3,c=-260)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-%283%29+%2B-+sqrt%28+3%5E2-4%2A1%2A%28-260%29+%29%29%2F%282%2A1%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-%283%29+%2B-+sqrt%28+3%5E2-4%2A1%2A%28-260%29+%29%29%2F%282%2A1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-3+%2B-+sqrt%28+9%2B1040+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%28-3+%2B-+sqrt%28+9%2B1040+%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-3+%2B-+sqrt%28+1049+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%28-3+%2B-+sqrt%28+1049+%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-3+%2B+sqrt%28+1049+%29%29%2F2+=+14.69 ALIGN=MIDDLE  ALT=\"x+=+%28-3+%2B+sqrt%28+1049+%29%29%2F2+=+14.69\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-3+-+sqrt%28+1049+%29%29%2F2=-17.69+ ALIGN=MIDDLE  ALT=\"x+=+%28-3+-+sqrt%28+1049+%29%29%2F2=-17.69+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  (reject this solution as the length can not be negative)<BR>\n" );
document.write( "Thus the length of the shorter leg is 14.69 units, and the length of the longer one is x+3=14.69+3=17.69 units<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );