document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=246102>Question 246102</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The hypotenuse of a right triangle is 2 units longer than the longer leg which is 14 units longer than the shorter leg.  Determine the lengths of the three sides.  How do i begin solving this question? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #179787 by </B><A HREF=/tutors/aboutme.mpl?userid=oberobic><B>oberobic(2304)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=oberobic><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=179787\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The Pythagorean Theorem is fundamental to the solution:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2+=+a%5E2+%2B+b%5E2 ALIGN=MIDDLE  ALT=\"c%5E2+=+a%5E2+%2B+b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ", where<BR>\n" );
document.write( "c = hypotenuse<BR>\n" );
document.write( "a = longer leg<BR>\n" );
document.write( "b = other leg<BR>\n" );
document.write( ".<BR>\n" );
document.write( "The problem setup gives you 3 important relationships.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+=+a+%2B+2 ALIGN=MIDDLE  ALT=\"c+=+a+%2B+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+b+%2B+14 ALIGN=MIDDLE  ALT=\"a+=+b+%2B+14\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "So,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+=+b+%2B+14+%2B+2+=+b+%2B+16 ALIGN=MIDDLE  ALT=\"c+=+b+%2B+14+%2B+2+=+b+%2B+16\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( ".<BR>\n" );
document.write( "Of course,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+b ALIGN=MIDDLE  ALT=\"b+=+b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Going back to the Pythagorean Theorem:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2+=+a%5E2+%2B+b%5E2 ALIGN=MIDDLE  ALT=\"c%5E2+=+a%5E2+%2B+b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "By substitution, we can cast the entire problem in terms of b, the shorter leg.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28b%2B16%29%5E2+=+%28b%2B14%29%5E2+%2B+b%5E2 ALIGN=MIDDLE  ALT=\"%28b%2B16%29%5E2+=+%28b%2B14%29%5E2+%2B+b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2+%2B+32b++%2B+256+=+b%5E2+%2B+28b+%2B+196+%2B+b%5E2+=+2b%5E2+%2B+28b+%2B+196 ALIGN=MIDDLE  ALT=\"b%5E2+%2B+32b++%2B+256+=+b%5E2+%2B+28b+%2B+196+%2B+b%5E2+=+2b%5E2+%2B+28b+%2B+196\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Subtract b^2 from both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=32b+%2B+256+=+b%5E2+%2B+28b+%2B+196 ALIGN=MIDDLE  ALT=\"32b+%2B+256+=+b%5E2+%2B+28b+%2B+196\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Subtract 32b from both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=256+=+b%5E2+-+4b+%2B+196 ALIGN=MIDDLE  ALT=\"256+=+b%5E2+-+4b+%2B+196\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Subtract 256 from both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+b%5E2+-+4b+-+60 ALIGN=MIDDLE  ALT=\"0+=+b%5E2+-+4b+-+60\"   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=b%5E2+-+4b+-+60+=+0 ALIGN=MIDDLE  ALT=\"b%5E2+-+4b+-+60+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Can we factor 60 such that the factors are 4 apart?  2*30? no 3*20? no. 4*15? no. 5*12? no.  6*10? yes!<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28b+-+10%29%28b+%2B+6%29+=+0 ALIGN=MIDDLE  ALT=\"%28b+-+10%29%28b+%2B+6%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Thus we have two candidate values for b:  10 and -6.   Since the leg of a triangle cannot be negative, the proposed solution is b = 10.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Substituting back into what we were told in the problem setup:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+b+%2B+14+=+24 ALIGN=MIDDLE  ALT=\"a+=+b+%2B+14+=+24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+=+a+%2B+2+=+26 ALIGN=MIDDLE  ALT=\"c+=+a+%2B+2+=+26\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "We always check our proposed solution.  Here we just use the Pythagorean Theorem again.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+=+24%2A24+=+576 ALIGN=MIDDLE  ALT=\"a%5E2+=+24%2A24+=+576\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E+2+=+10%2A10+=+100 ALIGN=MIDDLE  ALT=\"b%5E+2+=+10%2A10+=+100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+%2B+b%5E2+=+676 ALIGN=MIDDLE  ALT=\"a%5E2+%2B+b%5E2+=+676\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2+=+26%2A26+=+676 ALIGN=MIDDLE  ALT=\"c%5E2+=+26%2A26+=+676\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "That checks, so we have the correct answer.<BR>\n" );
document.write( "Done. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );