document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=980091>Question 980091</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The area of a triangle is 39 square ft. The length of one side is 1 ft more than teice the altitude to that side. Find the length of that side and the altitude to the side. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #601304 by </B><A HREF=/tutors/aboutme.mpl?userid=josh_jordan><B>josh_jordan(263)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josh_jordan><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=josh_jordan><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=601304\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To solve this, we first need to know the formula for the area of a triangle:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=%28bh%29%2F2 ALIGN=MIDDLE  ALT=\"A=%28bh%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, where A is Area, b is base (length of one side), and h is height (altitude)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We are told that the length of one side (base) is 1 ft more than twice the altitude.  In other words b = 2h + 1\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now, let's replace b in our formula for the area of a triangle with 2h + 1, and A with 39, since that's the area of the triangle:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%282h%2B1%29%28h%29%29%2F2=39 ALIGN=MIDDLE  ALT=\"%28%282h%2B1%29%28h%29%29%2F2=39\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We can now solve for h (altitude).  First, multiply both sides of this equation by 2, which will give us\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(2h + 1)(h) = 39 x 2 -----> (2h + 1)(h) = 78\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Next, multiply (2h + 1) by (h), giving us\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2h%5E2%2Bh=78 ALIGN=MIDDLE  ALT=\"2h%5E2%2Bh=78\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Third, subtract 78 from both sides and enter a 0 on the right side of the equal sign:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2h%5E2%2Bh-78=0 ALIGN=MIDDLE  ALT=\"2h%5E2%2Bh-78=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Fourth, factor this quadratic equation, which will give us:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282h%2B13%29%28h-6%29=0 ALIGN=MIDDLE  ALT=\"%282h%2B13%29%28h-6%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Fifth, set each set of parentheses equal to zero and solve for both values of h:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2h%2B13=0 ALIGN=MIDDLE  ALT=\"2h%2B13=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >-----><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2h=-13 ALIGN=MIDDLE  ALT=\"2h=-13\"   DISABLED_style= \"max-width:90%; height:auto;\" >-----><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=-13%2F2 ALIGN=MIDDLE  ALT=\"h=-13%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h-6=0 ALIGN=MIDDLE  ALT=\"h-6=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >-----><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=6 ALIGN=MIDDLE  ALT=\"h=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Since the height of a triangle cannot be a negative number, we can discard -13/2.  So, our altitude (height) is 6 feet.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "To find our length (base), replace the h in 2h + 1 with 6 and compute:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%286%29%2B1 ALIGN=MIDDLE  ALT=\"2%286%29%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >-----><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2B1 ALIGN=MIDDLE  ALT=\"12%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >-----><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13 ALIGN=MIDDLE  ALT=\"13\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Therefore, the length of this triangle is 13 feet and the altitude is 6 feet. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );