document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1053024>Question 1053024</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sides of the right triangular lot has a dimensions of (5x-11), (x) and (3x+4) meters respectively. What is the area of the lot? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #668316 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=668316\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The sides of the right triangular lot has a dimensions of (5x-11), (x) and (3x+4) meters respectively. What is the area of the lot?<BR>\n" );
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document.write( "For all sides to be >0, 5x-11>0 --> x>2.2<BR>\n" );
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document.write( "3x+4 > x for x>2.2, so x is not the hypotenuse.<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Either (3x+4)^2 + x^2 = (5x-11)^2<BR>\n" );
document.write( "or<BR>\n" );
document.write( "(3x+4)^2 = (5x-11)^2 + x^2<BR>\n" );
document.write( "================================<BR>\n" );
document.write( "Case 1: 5x-11 is the hypotenuse<BR>\n" );
document.write( "---<BR>\n" );
document.write( "(3x+4)^2 + x^2 = (5x-11)^2<BR>\n" );
document.write( "10x^2 + 24x + 16 = 25x^2 - 110x + 121<BR>\n" );
document.write( "15x^2 - 134x + 105 = 0<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=solve_quadratic_equation.solver>SOLVE quadratic equation (work shown, graph etc)</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=15x%5E2%2B-134x%2B105+=+0 ALIGN=MIDDLE  ALT=\"15x%5E2%2B-134x%2B105+=+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=%28-134%29%5E2-4%2A15%2A105=11656 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-134%29%5E2-4%2A15%2A105=11656\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=11656 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--134%2B-sqrt%28+11656+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--134%2B-sqrt%28+11656+%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-%28-134%29%2Bsqrt%28+11656+%29%29%2F2%5C15+=+8.06543188700421 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-134%29%2Bsqrt%28+11656+%29%29%2F2%5C15+=+8.06543188700421\"   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-%28-134%29-sqrt%28+11656+%29%29%2F2%5C15+=+0.867901446329125 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-134%29-sqrt%28+11656+%29%29%2F2%5C15+=+0.867901446329125\"   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=15x%5E2%2B-134x%2B105 ALIGN=MIDDLE  ALT=\"15x%5E2%2B-134x%2B105\"   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=15x%5E2%2B-134x%2B105+=+%28x-8.06543188700421%29%2A%28x-0.867901446329125%29 ALIGN=MIDDLE  ALT=\"15x%5E2%2B-134x%2B105+=+%28x-8.06543188700421%29%2A%28x-0.867901446329125%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 8.06543188700421, 0.867901446329125.\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+15%2Ax%5E2%2B-134%2Ax%2B105+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+15%2Ax%5E2%2B-134%2Ax%2B105+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "\n" );
document.write( "========<BR>\n" );
document.write( "x =~ 8.065<BR>\n" );
document.write( "x1 is rejected, it's less than 2.2<BR>\n" );
document.write( "====================<BR>\n" );
document.write( "Case 2: 3x+4 is the hypotenuse<BR>\n" );
document.write( "---<BR>\n" );
document.write( "(3x+4)^2 - x^2 = (5x-11)^2<BR>\n" );
document.write( "8x^2 + 24x + 16 = 25x^2 - 110x + 121<BR>\n" );
document.write( "17x^2 - 134x + 105 = 0<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=solve_quadratic_equation.solver>SOLVE quadratic equation (work shown, graph etc)</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=17x%5E2%2B-134x%2B105+=+0 ALIGN=MIDDLE  ALT=\"17x%5E2%2B-134x%2B105+=+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=%28-134%29%5E2-4%2A17%2A105=10816 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-134%29%5E2-4%2A17%2A105=10816\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=10816 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--134%2B-sqrt%28+10816+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--134%2B-sqrt%28+10816+%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-%28-134%29%2Bsqrt%28+10816+%29%29%2F2%5C17+=+7 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-134%29%2Bsqrt%28+10816+%29%29%2F2%5C17+=+7\"   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-%28-134%29-sqrt%28+10816+%29%29%2F2%5C17+=+0.882352941176471 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-134%29-sqrt%28+10816+%29%29%2F2%5C17+=+0.882352941176471\"   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=17x%5E2%2B-134x%2B105 ALIGN=MIDDLE  ALT=\"17x%5E2%2B-134x%2B105\"   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=17x%5E2%2B-134x%2B105+=+%28x-7%29%2A%28x-0.882352941176471%29 ALIGN=MIDDLE  ALT=\"17x%5E2%2B-134x%2B105+=+%28x-7%29%2A%28x-0.882352941176471%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 7, 0.882352941176471.\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+17%2Ax%5E2%2B-134%2Ax%2B105+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+17%2Ax%5E2%2B-134%2Ax%2B105+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "\n" );
document.write( "===========<BR>\n" );
document.write( "x = 7 ****** (the other solution is less then 2.2 and rejected)<BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "Use the 2 values of x to find the lengths of the 2 short sides, a & b<BR>\n" );
document.write( "Area = a*b/2<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );