document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=176017>Question 176017</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The base of a triangle is 8cm greater than the height. The area is 42cm^2. Find the height and length of the base. How do I set up this problem to get the answer? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #131134 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=131134\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let b=base and h=height\r<BR>\n" );
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document.write( "\"The base of a triangle is 8cm greater than the height\" means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=h%2B8 ALIGN=MIDDLE  ALT=\"b=h%2B8\"   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=A=%281%2F2%29bh ALIGN=MIDDLE  ALT=\"A=%281%2F2%29bh\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the area of a triangle formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=42=%281%2F2%29%28h%2B8%29h ALIGN=MIDDLE  ALT=\"42=%281%2F2%29%28h%2B8%29h\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=42 ALIGN=MIDDLE  ALT=\"A=42\"   DISABLED_style= \"max-width:90%; height:auto;\" > (the given area) and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=h%2B8 ALIGN=MIDDLE  ALT=\"b=h%2B8\"   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=42%2A2=%28h%2B8%29h ALIGN=MIDDLE  ALT=\"42%2A2=%28h%2B8%29h\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by 2.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=84=%28h%2B8%29h ALIGN=MIDDLE  ALT=\"84=%28h%2B8%29h\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=84=h%28h%2B8%29 ALIGN=MIDDLE  ALT=\"84=h%28h%2B8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=84=h%5E2%2B8h ALIGN=MIDDLE  ALT=\"84=h%5E2%2B8h\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=h%5E2%2B8h-84 ALIGN=MIDDLE  ALT=\"0=h%5E2%2B8h-84\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 84 from both sides.\r<BR>\n" );
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document.write( "Notice we have a quadratic equation in the form of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ah%5E2%2Bbh%2Bc ALIGN=MIDDLE  ALT=\"ah%5E2%2Bbh%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1 ALIGN=MIDDLE  ALT=\"a=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=8 ALIGN=MIDDLE  ALT=\"b=8\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-84 ALIGN=MIDDLE  ALT=\"c=-84\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Let's use the quadratic formula to solve for h\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"h+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the quadratic formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+=+%28-%288%29+%2B-+sqrt%28+%288%29%5E2-4%281%29%28-84%29+%29%29%2F%282%281%29%29 ALIGN=MIDDLE  ALT=\"h+=+%28-%288%29+%2B-+sqrt%28+%288%29%5E2-4%281%29%28-84%29+%29%29%2F%282%281%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1 ALIGN=MIDDLE  ALT=\"a=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=8 ALIGN=MIDDLE  ALT=\"b=8\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-84 ALIGN=MIDDLE  ALT=\"c=-84\"   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=h+=+%28-8+%2B-+sqrt%28+64-4%281%29%28-84%29+%29%29%2F%282%281%29%29 ALIGN=MIDDLE  ALT=\"h+=+%28-8+%2B-+sqrt%28+64-4%281%29%28-84%29+%29%29%2F%282%281%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8 ALIGN=MIDDLE  ALT=\"8\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64 ALIGN=MIDDLE  ALT=\"64\"   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=h+=+%28-8+%2B-+sqrt%28+64--336+%29%29%2F%282%281%29%29 ALIGN=MIDDLE  ALT=\"h+=+%28-8+%2B-+sqrt%28+64--336+%29%29%2F%282%281%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%281%29%28-84%29 ALIGN=MIDDLE  ALT=\"4%281%29%28-84%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-336 ALIGN=MIDDLE  ALT=\"-336\"   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=h+=+%28-8+%2B-+sqrt%28+64%2B336+%29%29%2F%282%281%29%29 ALIGN=MIDDLE  ALT=\"h+=+%28-8+%2B-+sqrt%28+64%2B336+%29%29%2F%282%281%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2864--336%29 ALIGN=MIDDLE  ALT=\"sqrt%2864--336%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2864%2B336%29 ALIGN=MIDDLE  ALT=\"sqrt%2864%2B336%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=h+=+%28-8+%2B-+sqrt%28+400+%29%29%2F%282%281%29%29 ALIGN=MIDDLE  ALT=\"h+=+%28-8+%2B-+sqrt%28+400+%29%29%2F%282%281%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64 ALIGN=MIDDLE  ALT=\"64\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=336 ALIGN=MIDDLE  ALT=\"336\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=400 ALIGN=MIDDLE  ALT=\"400\"   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=h+=+%28-8+%2B-+sqrt%28+400+%29%29%2F%282%29 ALIGN=MIDDLE  ALT=\"h+=+%28-8+%2B-+sqrt%28+400+%29%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   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=h+=+%28-8+%2B-+20%29%2F%282%29 ALIGN=MIDDLE  ALT=\"h+=+%28-8+%2B-+20%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=400 ALIGN=MIDDLE  ALT=\"400\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20 ALIGN=MIDDLE  ALT=\"20\"   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=h+=+%28-8+%2B+20%29%2F%282%29 ALIGN=MIDDLE  ALT=\"h+=+%28-8+%2B+20%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+=+%28-8+-+20%29%2F%282%29 ALIGN=MIDDLE  ALT=\"h+=+%28-8+-+20%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the expression. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+=+%2812%29%2F%282%29 ALIGN=MIDDLE  ALT=\"h+=+%2812%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+=++%28-28%29%2F%282%29 ALIGN=MIDDLE  ALT=\"h+=++%28-28%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms. \r<BR>\n" );
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document.write( "<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;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+=+-14 ALIGN=MIDDLE  ALT=\"h+=+-14\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify. \r<BR>\n" );
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document.write( "So the possible answers are <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;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+=+-14 ALIGN=MIDDLE  ALT=\"h+=+-14\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "However, since a negative height is not possible, this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+=+-14 ALIGN=MIDDLE  ALT=\"h+=+-14\"   DISABLED_style= \"max-width:90%; height:auto;\" > is NOT a solution\r<BR>\n" );
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document.write( "So the only answer for the height is <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;\" > which means that the height is 6 cm.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=h%2B8 ALIGN=MIDDLE  ALT=\"b=h%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Go back to the first equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=6%2B8 ALIGN=MIDDLE  ALT=\"b=6%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <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" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=14 ALIGN=MIDDLE  ALT=\"b=14\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add. So the base is 14 cm.\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So the base is 14 cm and the height is 6 cm </SPAN>\n" );
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