document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=291783>Question 291783</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The length of one leg of a right triangle is 2 cm less than three times the length of other leg. The area of the triangle is 48 cm^2. Find the length of each leg. Please show work! thank u </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #210921 by </B><A HREF=/tutors/aboutme.mpl?userid=eggsarecool><B>eggsarecool(46)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=eggsarecool><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=210921\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Ok so lets call one leg x<BR>\n" );
document.write( "The other leg is three times the length 3x and 2 cm less so 3x-2.<BR>\n" );
document.write( "The Area of a triangle is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=%281%2F2%29%2Ab%2Ah ALIGN=MIDDLE  ALT=\"A=%281%2F2%29%2Ab%2Ah\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "For a right Triangle the base is one leg and the height is the other leg.<BR>\n" );
document.write( "We also know that the Area is 48. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=48 ALIGN=MIDDLE  ALT=\"A=48\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=48=%281%2F2%29%2Ax%283x-2%29.+x+is+one+side%2Fleg%2C+and+3x-2+is+the+other+side%2Fleg%0D%0A%7B%7B%7B48=%281%2F2%29%2A%283x%5E2-2x%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply by 2 to cancel the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=96=3x%5E2-2x ALIGN=MIDDLE  ALT=\"96=3x%5E2-2x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 96 from both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2-3x-96=0 ALIGN=MIDDLE  ALT=\"3x%5E2-3x-96=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor out the 3.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28x%5E2-x-32%29=0 ALIGN=MIDDLE  ALT=\"3%28x%5E2-x-32%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Use the qudratic formula to solve/<BR>\n" );
document.write( "<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=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%5E2%2B-1x%2B-32+=+0 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-1x%2B-32+=+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=x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"x%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=%28-1%29%5E2-4%2A1%2A-32=129 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-1%29%5E2-4%2A1%2A-32=129\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=129 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--1%2B-sqrt%28+129+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--1%2B-sqrt%28+129+%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=x%5B1%5D+=+%28-%28-1%29%2Bsqrt%28+129+%29%29%2F2%5C1+=+6.17890834580027 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-1%29%2Bsqrt%28+129+%29%29%2F2%5C1+=+6.17890834580027\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+%28-%28-1%29-sqrt%28+129+%29%29%2F2%5C1+=+-5.17890834580027 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-1%29-sqrt%28+129+%29%29%2F2%5C1+=+-5.17890834580027\"   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=1x%5E2%2B-1x%2B-32 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-1x%2B-32\"   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=1x%5E2%2B-1x%2B-32+=+1%28x-6.17890834580027%29%2A%28x--5.17890834580027%29 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-1x%2B-32+=+1%28x-6.17890834580027%29%2A%28x--5.17890834580027%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 6.17890834580027, -5.17890834580027.\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+1%2Ax%5E2%2B-1%2Ax%2B-32+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-1%2Ax%2B-32+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "And since you cannot have a negative length in a triangle, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6.17890834580027 ALIGN=MIDDLE  ALT=\"6.17890834580027\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the length of the leg we called x. To find the length of the other leg multiply by 3 and then subtract 2 to get the length of the other leg.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2A6.17890834580027-2=16.53672503740081 ALIGN=MIDDLE  ALT=\"3%2A6.17890834580027-2=16.53672503740081\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So the length of the other leg is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16.53672503740081 ALIGN=MIDDLE  ALT=\"16.53672503740081\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );