document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=952453>Question 952453</A>: <I><SPAN STYLE=\"word-break: break-all;\"> IN A RIGHT TRIANGLE, THE HYPOTENUSE IS 1 FOOT MORE THAN THE LONG LEG, WHILE THE SHORT LEG IS 11FT. LESS THAN HALF THE LONG LEG. YOUR GOAL IS TO FIND THE PERIMETER OF THIS TRIANGLE.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #581655 by </B><A HREF=/tutors/aboutme.mpl?userid=macston><B>macston(5194)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=macston><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=macston><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=581655\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> b=long leg; a=short leg=(0.5b)-11ft; c=hypotenuse=b+1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2Bb%5E2=c%5E2 ALIGN=MIDDLE  ALT=\"a%5E2%2Bb%5E2=c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Substitute for a and c, solve for b<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.25b%5E2-11b%2B121%2Bb%5E2=b%5E2%2B2b%2B1 ALIGN=MIDDLE  ALT=\".25b%5E2-11b%2B121%2Bb%5E2=b%5E2%2B2b%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.25b%5E2-11b%2B121=b%5E2%2B2b%2B1 ALIGN=MIDDLE  ALT=\"1.25b%5E2-11b%2B121=b%5E2%2B2b%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >Subtract<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28b%5E2%2B2b%2B1%29 ALIGN=MIDDLE  ALT=\"%28b%5E2%2B2b%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > from each side.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.25b%5E2-13b%2B120=0 ALIGN=MIDDLE  ALT=\"0.25b%5E2-13b%2B120=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><TABLE  BORDER=1>\n" );
document.write( "\n" );
document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=quadratic.solver>SOLVE quadratic equation with variable</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ab%5E2%2Bbb%2Bc=0 ALIGN=MIDDLE  ALT=\"ab%5E2%2Bbb%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.25b%5E2%2B-13b%2B120+=+0 ALIGN=MIDDLE  ALT=\"0.25b%5E2%2B-13b%2B120+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"b%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For these solutions to exist, the <U>discriminant</U> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be a negative number.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  First, we need to compute the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%28-13%29%5E2-4%2A0.25%2A120=49 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-13%29%5E2-4%2A0.25%2A120=49\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=49 is greater than zero. That means that there are two solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B12%5D+=+%28--13%2B-sqrt%28+49+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--13%2B-sqrt%28+49+%29%29%2F2%5Ca\"   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%5B1%5D+=+%28-%28-13%29%2Bsqrt%28+49+%29%29%2F2%5C0.25+=+40 ALIGN=MIDDLE  ALT=\"b%5B1%5D+=+%28-%28-13%29%2Bsqrt%28+49+%29%29%2F2%5C0.25+=+40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5B2%5D+=+%28-%28-13%29-sqrt%28+49+%29%29%2F2%5C0.25+=+12 ALIGN=MIDDLE  ALT=\"b%5B2%5D+=+%28-%28-13%29-sqrt%28+49+%29%29%2F2%5C0.25+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <BR>\n" );
document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.25b%5E2%2B-13b%2B120 ALIGN=MIDDLE  ALT=\"0.25b%5E2%2B-13b%2B120\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be factored:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.25b%5E2%2B-13b%2B120+=+0.25%28b-40%29%2A%28b-12%29 ALIGN=MIDDLE  ALT=\"0.25b%5E2%2B-13b%2B120+=+0.25%28b-40%29%2A%28b-12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 40, 12.\n" );
document.write( "Here's your graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+0.25%2Ax%5E2%2B-13%2Ax%2B120+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+0.25%2Ax%5E2%2B-13%2Ax%2B120+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "\n" );
document.write( "b=40 or b=12 (long leg)<BR>\n" );
document.write( "For b=40:<BR>\n" );
document.write( "a=0.5b-11ft=0.5(40)-11 ft=9 ft (short leg)<BR>\n" );
document.write( "c=b+1=40ft+1 ft=41 ft(hypotenuse)<BR>\n" );
document.write( "For b=12<BR>\n" );
document.write( "a=.5(12)-11 ft=6-11=-5ft does not work<BR>\n" );
document.write( "ANSWER 1: The long leg is 40 feet.<BR>\n" );
document.write( "ANSWER 2: The short leg is 9 feet.<BR>\n" );
document.write( "ANSWER 3: The hypotenuse is 41 feet.<BR>\n" );
document.write( "CHECK:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2Bb%5E2=c%5E2 ALIGN=MIDDLE  ALT=\"a%5E2%2Bb%5E2=c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289+ft%29%5E2%2B%2840+ft%29%5E2=%2841+ft%29%5E2 ALIGN=MIDDLE  ALT=\"%289+ft%29%5E2%2B%2840+ft%29%5E2=%2841+ft%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=81ft%5E2%2B1600ft%5E2=1681ft%5E2 ALIGN=MIDDLE  ALT=\"81ft%5E2%2B1600ft%5E2=1681ft%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1681ft%5E2=1681ft%5E2 ALIGN=MIDDLE  ALT=\"1681ft%5E2=1681ft%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );