document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=746903>Question 746903</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The height of a right triangle is 5 units more than twice its base. If the area of the triangle is 21 square units, what is its height?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #454567 by </B><A HREF=/tutors/aboutme.mpl?userid=timvanswearingen><B>timvanswearingen(106)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=timvanswearingen><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=timvanswearingen><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=454567\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x represent the length of the base.\r<BR>\n" );
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document.write( "Then the height can be represented as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=2x%2B5 ALIGN=MIDDLE  ALT=\"h=2x%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" > (5 units more than twice the base)\r<BR>\n" );
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document.write( "Now, the formula for the area of a triangle is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=b%2Ah ALIGN=MIDDLE  ALT=\"A=b%2Ah\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=21=%281%2F2%29%2Ax%2A%282x%2B5%29 ALIGN=MIDDLE  ALT=\"21=%281%2F2%29%2Ax%2A%282x%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Using the distributive property,<BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=21=x%5E2%2B%285%2F2%29x ALIGN=MIDDLE  ALT=\"21=x%5E2%2B%285%2F2%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Subtract 21 from both sides, \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=x%5E2%2B%285%2F2%29x-21 ALIGN=MIDDLE  ALT=\"0=x%5E2%2B%285%2F2%29x-21\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now, using a=1, b=5/2, and c=-21, plug into the quadratic formula.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%285%2F2+%2B-+sqrt%28+%285%2F2%29%5E2-4%2A%282%29%2A%28-21+%29%29%29%2F%282%2A%282%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%282.5+%2B-+sqrt%28+6.25%2B168+%29%29%2F4+ ALIGN=MIDDLE  ALT=\"x+=+%282.5+%2B-+sqrt%28+6.25%2B168+%29%29%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%282.5+%2B-+sqrt%28+174.25+%29%29%2F4+ ALIGN=MIDDLE  ALT=\"x+=+%282.5+%2B-+sqrt%28+174.25+%29%29%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "There are two possible answers.  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%282.5%2B+sqrt%28+174.25+%29%29%2F4 ALIGN=MIDDLE  ALT=\"x=%282.5%2B+sqrt%28+174.25+%29%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%282.5-+sqrt%28+174.25+%29%29%2F4 ALIGN=MIDDLE  ALT=\"x=%282.5-+sqrt%28+174.25+%29%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The second answer would result in a negative number.  Since we are trying to find out the length of the base of a triangle, we can throw out the negative answer.  \r<BR>\n" );
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document.write( "Thus, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%282.5%2B+sqrt%28+174.25+%29%29%2F4 ALIGN=MIDDLE  ALT=\"x=%282.5%2B+sqrt%28+174.25+%29%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So x is about 3.925 units.  \r<BR>\n" );
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document.write( "x was representing the base.  Since the height was 2x+5, simply plug in the x value found above to find the height.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=2x%2B5 ALIGN=MIDDLE  ALT=\"h=2x%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=2%2A%283.925%29%2B5 ALIGN=MIDDLE  ALT=\"h=2%2A%283.925%29%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=7.850%2B5 ALIGN=MIDDLE  ALT=\"h=7.850%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "h=12.850 units\r<BR>\n" );
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