document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=333636>Question 333636</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am having a lot of trouble with this question: \"The area of a rectangle is 528 sq mm. The base is 8 more than three times the height. What is the perimeter?\" I started the problem by setting up this equation: 528=h(3h+8) where h=height. Then I got 528=3h^2+8h. However, I'm not sure what to do after this. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #239051 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=239051\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=528=3h%5E2%2B8h ALIGN=MIDDLE  ALT=\"528=3h%5E2%2B8h\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=3h%5E2%2B8h-528 ALIGN=MIDDLE  ALT=\"0=3h%5E2%2B8h-528\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 528 from both sides.\r<BR>\n" );
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document.write( "Notice that the quadratic <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3h%5E2%2B8h-528 ALIGN=MIDDLE  ALT=\"3h%5E2%2B8h-528\"   DISABLED_style= \"max-width:90%; height:auto;\" > is 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=3 ALIGN=MIDDLE  ALT=\"A=3\"   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=-528 ALIGN=MIDDLE  ALT=\"C=-528\"   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%283%29%28-528%29+%29%29%2F%282%283%29%29 ALIGN=MIDDLE  ALT=\"h+=+%28-%288%29+%2B-+sqrt%28+%288%29%5E2-4%283%29%28-528%29+%29%29%2F%282%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=3 ALIGN=MIDDLE  ALT=\"A=3\"   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=-528 ALIGN=MIDDLE  ALT=\"C=-528\"   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%283%29%28-528%29+%29%29%2F%282%283%29%29 ALIGN=MIDDLE  ALT=\"h+=+%28-8+%2B-+sqrt%28+64-4%283%29%28-528%29+%29%29%2F%282%283%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--6336+%29%29%2F%282%283%29%29 ALIGN=MIDDLE  ALT=\"h+=+%28-8+%2B-+sqrt%28+64--6336+%29%29%2F%282%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%283%29%28-528%29 ALIGN=MIDDLE  ALT=\"4%283%29%28-528%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6336 ALIGN=MIDDLE  ALT=\"-6336\"   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%2B6336+%29%29%2F%282%283%29%29 ALIGN=MIDDLE  ALT=\"h+=+%28-8+%2B-+sqrt%28+64%2B6336+%29%29%2F%282%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2864--6336%29 ALIGN=MIDDLE  ALT=\"sqrt%2864--6336%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2864%2B6336%29 ALIGN=MIDDLE  ALT=\"sqrt%2864%2B6336%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+6400+%29%29%2F%282%283%29%29 ALIGN=MIDDLE  ALT=\"h+=+%28-8+%2B-+sqrt%28+6400+%29%29%2F%282%283%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=6336 ALIGN=MIDDLE  ALT=\"6336\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6400 ALIGN=MIDDLE  ALT=\"6400\"   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+6400+%29%29%2F%286%29 ALIGN=MIDDLE  ALT=\"h+=+%28-8+%2B-+sqrt%28+6400+%29%29%2F%286%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=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"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=h+=+%28-8+%2B-+80%29%2F%286%29 ALIGN=MIDDLE  ALT=\"h+=+%28-8+%2B-+80%29%2F%286%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=6400 ALIGN=MIDDLE  ALT=\"6400\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=80 ALIGN=MIDDLE  ALT=\"80\"   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+80%29%2F%286%29 ALIGN=MIDDLE  ALT=\"h+=+%28-8+%2B+80%29%2F%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+=+%28-8+-+80%29%2F%286%29 ALIGN=MIDDLE  ALT=\"h+=+%28-8+-+80%29%2F%286%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+=+%2872%29%2F%286%29 ALIGN=MIDDLE  ALT=\"h+=+%2872%29%2F%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+=++%28-88%29%2F%286%29 ALIGN=MIDDLE  ALT=\"h+=++%28-88%29%2F%286%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+=+12 ALIGN=MIDDLE  ALT=\"h+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+=+-44%2F3 ALIGN=MIDDLE  ALT=\"h+=+-44%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify. \r<BR>\n" );
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document.write( "So the solutions are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+=+12 ALIGN=MIDDLE  ALT=\"h+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+=+-44%2F3 ALIGN=MIDDLE  ALT=\"h+=+-44%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "  \r<BR>\n" );
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document.write( "However, a negative height doesn't make any sense. So we'll ignore <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+=+-44%2F3 ALIGN=MIDDLE  ALT=\"h+=+-44%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This means that the height is 12 mm.\r<BR>\n" );
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document.write( "I'll let you use this info to find the perimeter. </SPAN>\n" );
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