document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=21412>Question 21412</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This is a geometry question, from my algebra class, we are working on quadatric equations.  Iam so confused.   I know the formula for area of a triangle.    A = 1/2 b x h.   But can't figure out how to come up with an equation to figure out how to do this.\r<BR>\n" );
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document.write( "The question:<BR>\n" );
document.write( "The base of a triangle is 4 feet less than 3 times the height, and the area is 16 square feet.   Find the dimensions of the triangle (Note:  need to set up an equation to sove the problem)   Please help!!  Thank you.    </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #10328 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=10328\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let  h = the height<BR>\n" );
document.write( "let b = the base<BR>\n" );
document.write( "let A = the area\r<BR>\n" );
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document.write( "A = 16 = (1/2)*b*h\r<BR>\n" );
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document.write( "multiply each side by 2<BR>\n" );
document.write( "(a) 32 = b*h\r<BR>\n" );
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document.write( "from the description of the problem, <BR>\n" );
document.write( "b = 3*h - 4<BR>\n" );
document.write( "substitute this result for b into (a)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=32+=+%283%2Ah+-+4%29%2Ah ALIGN=MIDDLE  ALT=\"32+=+%283%2Ah+-+4%29%2Ah\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=32+=+3%2Ah%5E2+-4%2Ah ALIGN=MIDDLE  ALT=\"32+=+3%2Ah%5E2+-4%2Ah\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "rearranging,<BR>\n" );
document.write( "(b) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Ah%5E2+-+4%2Ah+-+32+=+0 ALIGN=MIDDLE  ALT=\"3%2Ah%5E2+-+4%2Ah+-+32+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "this is a quadratic equation<BR>\n" );
document.write( "the roots (negative and positive) are given by<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28-b+%2B-sqrt%28b%5E2+-+4%2Aa%2Ac%29%29%2F%282%2Aa%29 ALIGN=MIDDLE  ALT=\"+%28-b+%2B-sqrt%28b%5E2+-+4%2Aa%2Ac%29%29%2F%282%2Aa%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "if the form of the equation is<BR>\n" );
document.write( "a*h^2 + bh + c = 0<BR>\n" );
document.write( "from our result in (b), <BR>\n" );
document.write( "a = 3<BR>\n" );
document.write( "b = -4<BR>\n" );
document.write( "c = -32\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-%28-4%29+%2B-+sqrt%2816+-+%284+%2A3%2A%28-32%29%29%29%29%2F%282%2A3%29 ALIGN=MIDDLE  ALT=\"%28-%28-4%29+%2B-+sqrt%2816+-+%284+%2A3%2A%28-32%29%29%29%29%2F%282%2A3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284+%2B-+sqrt%2816+%2B+384%29%29%2F6+ ALIGN=MIDDLE  ALT=\"%284+%2B-+sqrt%2816+%2B+384%29%29%2F6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284+%2B-+sqrt%28400%29%29%2F6+ ALIGN=MIDDLE  ALT=\"%284+%2B-+sqrt%28400%29%29%2F6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284+%2B-+20%29%2F6+ ALIGN=MIDDLE  ALT=\"%284+%2B-+20%29%2F6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "choose the positive result<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284+%2B+20%29%2F6+ ALIGN=MIDDLE  ALT=\"%284+%2B+20%29%2F6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4+=+r1 ALIGN=MIDDLE  ALT=\"4+=+r1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "therefore h = 4<BR>\n" );
document.write( "32 = b*h<BR>\n" );
document.write( "b = 32/4<BR>\n" );
document.write( "b = 8<BR>\n" );
document.write( "substitute these values back into<BR>\n" );
document.write( "b = 3*h - 4<BR>\n" );
document.write( "A = (1/2)*b*h<BR>\n" );
document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );