document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=212968>Question 212968</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The hypotenuse of a right triangle is twice as long as one of the legs and 4 inches longer than the other. What are the lengths of the sides of the triangle? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #160883 by </B><A HREF=/tutors/aboutme.mpl?userid=vleith><B>vleith(2983)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=vleith><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=160883\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let h be the length of the hypotenuse. Then one side is h/2 and the third side is h-4.<BR>\n" );
document.write( "Since it is a right triangle, you know that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5E2+=+%28h%2F2%29%5E2+%2B+%28h-4%29%5E2 ALIGN=MIDDLE  ALT=\"h%5E2+=+%28h%2F2%29%5E2+%2B+%28h-4%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=h%5E2+=+h%5E2%2F4+%2B+h%5E2+-8h+%2B+16 ALIGN=MIDDLE  ALT=\"h%5E2+=+h%5E2%2F4+%2B+h%5E2+-8h+%2B+16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+h%5E2%2F4+-+8h+%2B+16 ALIGN=MIDDLE  ALT=\"0+=+h%5E2%2F4+-+8h+%2B+16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+h%5E2+-+32h+%2B+64 ALIGN=MIDDLE  ALT=\"0+=+h%5E2+-+32h+%2B+64\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Use the quadratic equation to solve<BR>\n" );
document.write( "<TABLE  BORDER=1>\n" );
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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-32x%2B64+=+0 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-32x%2B64+=+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=%28-32%29%5E2-4%2A1%2A64=768 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-32%29%5E2-4%2A1%2A64=768\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=768 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--32%2B-sqrt%28+768+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--32%2B-sqrt%28+768+%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-%28-32%29%2Bsqrt%28+768+%29%29%2F2%5C1+=+29.856406460551 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-32%29%2Bsqrt%28+768+%29%29%2F2%5C1+=+29.856406460551\"   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-%28-32%29-sqrt%28+768+%29%29%2F2%5C1+=+2.14359353944898 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-32%29-sqrt%28+768+%29%29%2F2%5C1+=+2.14359353944898\"   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-32x%2B64 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-32x%2B64\"   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-32x%2B64+=+1%28x-29.856406460551%29%2A%28x-2.14359353944898%29 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-32x%2B64+=+1%28x-29.856406460551%29%2A%28x-2.14359353944898%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 29.856406460551, 2.14359353944898.\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-32%2Ax%2B64+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-32%2Ax%2B64+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
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document.write( "Since one of the answer is too short to make that number -4 positive, the hypotenuse is ~29.85<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );