document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=287323>Question 287323</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1. One leg of a right triangle is 2 feet longer than the other leg. The hypotenuse is 10 feet long. Find the length of the legs of the triangle? \r<BR>\n" );
document.write( "\n" );
document.write( "2. One leg of the right triangle is 5 units. The hypotenuse is one unit longer than the other leg. What is the length of the hypotenuse and the other leg? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #208254 by </B><A HREF=/tutors/aboutme.mpl?userid=PRMath><B>PRMath(133)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=PRMath><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=208254\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. One leg of a right triangle is 2 feet longer than the other leg. The hypotenuse is 10 feet long. Find the length of the legs of the triangle? \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "One leg of the right triangle is unknown:  We'll call it \"x\"<BR>\n" );
document.write( "The other leg is 2 feet longer than the other leg:  2 + x<BR>\n" );
document.write( "The hypotenuse is 10 feet long.  \r<BR>\n" );
document.write( "\n" );
document.write( "You know <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+%2B+b%5E2=+c%5E2 ALIGN=MIDDLE  ALT=\"a%5E2+%2B+b%5E2=+c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > (\"c\" is the hypotenuse). Now let's fill in the blank.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now let's fill in what we know.  <BR>\n" );
document.write( "One leg is \"x\"<BR>\n" );
document.write( "The other leg: 2 + x<BR>\n" );
document.write( "The hypot. is:  10\r<BR>\n" );
document.write( "<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+%2B+%28x%2B2%29%5E2+=+10%5E2 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+%28x%2B2%29%5E2+=+10%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+x%5E2+%2B+4x+%2B+4+=+10%5E2 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+x%5E2+%2B+4x+%2B+4+=+10%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > (FOILED the above)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2+%2B+4x+%2B+4+=+100 ALIGN=MIDDLE  ALT=\"2x%5E2+%2B+4x+%2B+4+=+100\"   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+%2B+4x+%2B+4+-+100+=+0 ALIGN=MIDDLE  ALT=\"2x%5E2+%2B+4x+%2B+4+-+100+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (subtracted 100 from both sides of the equation)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2+%2B+4x+-+96+=+0 ALIGN=MIDDLE  ALT=\"2x%5E2+%2B+4x+-+96+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (combined like terms)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28x%5E2+%2B+2x+-+48%29+=+0 ALIGN=MIDDLE  ALT=\"2%28x%5E2+%2B+2x+-+48%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (factored out a 2 from everything)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+2x+-+48%29+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+2x+-+48%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (divided 2 from both sides of the equation)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+%2B+8%29%28x+-+6%29 ALIGN=MIDDLE  ALT=\"%28x+%2B+8%29%28x+-+6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0 <BR>\n" );
document.write( "x = -8 or x = 6 (disregard the -8 because a side cannot equal -8)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Does this work?  If one side is 6 and the other is 2 more than 6 (or 8) and the hypotenuse is 10, then we have:  \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%5E2+%2B+8%5E2+=+10%5E2 ALIGN=MIDDLE  ALT=\"6%5E2+%2B+8%5E2+=+10%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36+%2B+64+=+100 ALIGN=MIDDLE  ALT=\"36+%2B+64+=+100\"   DISABLED_style= \"max-width:90%; height:auto;\" >} YAY it works.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2. One leg of the right triangle is 5 units. The hypotenuse is one unit longer than the other leg. What is the length of the hypotenuse and the other leg?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "One leg is 5 units:  5<BR>\n" );
document.write( "The hypotenuse is 1 longer than the other leg:  X+ 1<BR>\n" );
document.write( "The other leg is: X\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Put it all together:\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+%2B+5%5E2+=+%28x+%2B+1%29%5E2 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+5%5E2+=+%28x+%2B+1%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+25+=+x%5E2+%2B+2x+%2B+1 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+25+=+x%5E2+%2B+2x+%2B+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+x%5E2+-+x%5E2+%2B+2x+%2B+1+-+25 ALIGN=MIDDLE  ALT=\"0+=+x%5E2+-+x%5E2+%2B+2x+%2B+1+-+25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+2x+-24 ALIGN=MIDDLE  ALT=\"0+=+2x+-24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+2%28x+-+12%29 ALIGN=MIDDLE  ALT=\"0+=+2%28x+-+12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+x+-+12 ALIGN=MIDDLE  ALT=\"0+=+x+-+12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12+=+x ALIGN=MIDDLE  ALT=\"12+=+x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Does x = 12 work?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "One leg is 5<BR>\n" );
document.write( "The other is 12<BR>\n" );
document.write( "the hypotenuse is one more than 12:  this is 13\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%5E2+%2B+12%5E2+=+13%5E2 ALIGN=MIDDLE  ALT=\"5%5E2+%2B+12%5E2+=+13%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25+%2B+144+=+169 ALIGN=MIDDLE  ALT=\"25+%2B+144+=+169\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=169+=+169 ALIGN=MIDDLE  ALT=\"169+=+169\"   DISABLED_style= \"max-width:90%; height:auto;\" >  YAY this works, too.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "I hope this helps you. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );