document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=166492>Question 166492</A>: <I><SPAN STYLE=\"word-break: break-all;\"> please help me solve this problem.\r<BR>\n" );
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document.write( "the area of a triangle is 13.5 meters. Find the base and height of the retangle <BR>\n" );
document.write( "if its height is 6 meters greaster than it's base. Use an equation and the formula    area of a triangle =0.5(base)(height). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #122697 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><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=122697\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A = (b*h)/2 (equation 1)<BR>\n" );
document.write( "where A = area<BR>\n" );
document.write( "b = base<BR>\n" );
document.write( "h = height<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "h = b+6 (given)<BR>\n" );
document.write( "A = 13.5 (given)<BR>\n" );
document.write( "equation 1 becomes:<BR>\n" );
document.write( "A = [b*(b+6)]/2 = 13.5<BR>\n" );
document.write( "which becomes:<BR>\n" );
document.write( "[b*(b+6)]/2 = 13.5 (equation 2)<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "multiply both sides of equation 2 by 2:<BR>\n" );
document.write( "b*(b+6) = 27<BR>\n" );
document.write( "simplify:<BR>\n" );
document.write( "b^2 + 6*b = 27<BR>\n" );
document.write( "complete the squares:<BR>\n" );
document.write( "(b+3)^2 = 27 + 9 (explanation for this down below after the answer)<BR>\n" );
document.write( "simplify:<BR>\n" );
document.write( "(b+3)^2 = 36<BR>\n" );
document.write( "take square root of both sides:<BR>\n" );
document.write( "b+3 = +/- 6<BR>\n" );
document.write( "subtract 3 from both sides:<BR>\n" );
document.write( "b = +/- 6 - 3<BR>\n" );
document.write( "b becomes either:<BR>\n" );
document.write( "6-3 = 3<BR>\n" );
document.write( "or:<BR>\n" );
document.write( "-6-3 = -9<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "since b can't be negative, answer has to be:<BR>\n" );
document.write( "b = 3<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "since h = b+6, then:<BR>\n" );
document.write( "h = 9<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "you have:<BR>\n" );
document.write( "b = 3<BR>\n" );
document.write( "h = 9<BR>\n" );
document.write( "A = 13.5 (given)<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "substitute in equation 1:<BR>\n" );
document.write( "A = (b*h)/2 (equation 1)<BR>\n" );
document.write( "A = (3*9)/2 = 13.5<BR>\n" );
document.write( "A = 27/2 = 13.5<BR>\n" );
document.write( "A = 13.5 = 13.5<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "values for b and h prove out.<BR>\n" );
document.write( "equation is good.<BR>\n" );
document.write( "b = 3<BR>\n" );
document.write( "h = 9<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "explanation for completing the squares is shown below:<BR>\n" );
document.write( "also shown below is the fact that you could have also solved this using the quadratic formula.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "in order to complete the squares of your equation:<BR>\n" );
document.write( "b^2 + 6*b)<BR>\n" );
document.write( "i took half of the 6 and turned the equation into:<BR>\n" );
document.write( "(b+3)^2<BR>\n" );
document.write( "if you multiply this out, you will get:<BR>\n" );
document.write( "b^2 + 6*b + 9<BR>\n" );
document.write( "there's an extra 9 in there.<BR>\n" );
document.write( "in order to keep the equations in balance i had to add 9 to the other side of the equation.<BR>\n" );
document.write( "that's why the equation went from:<BR>\n" );
document.write( "b^2 + 6*b = 27<BR>\n" );
document.write( "to:<BR>\n" );
document.write( "(b+3)^2 = 27 + 9<BR>\n" );
document.write( "the additional 9 on the right hand side of the equation kept them in balance because i added 9 to the left hand side by completing the squares.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "use of the quadratic formula instead.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "rather than completing the squares, you can also solve this equation using the quadratic formula.<BR>\n" );
document.write( "the equation to solve was:<BR>\n" );
document.write( "b^2 + 6*b = 27<BR>\n" );
document.write( "subtract 27 from both sides of the equation:<BR>\n" );
document.write( "b^2 + 6*b - 27 = 0<BR>\n" );
document.write( "let x = b (this is necessary because general form of quadratic equation and quadratic formula use b for another purpose)<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "formula becomes:<BR>\n" );
document.write( "x^2 + 6*x - 27 = 0<BR>\n" );
document.write( "general form of quadratic equation is:<BR>\n" );
document.write( "a*x^2 + b*x + c = 0<BR>\n" );
document.write( "the quadratic formula can be used to solve this quadratic equation.<BR>\n" );
document.write( "general form of quadratic formula is: x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a = 1<BR>\n" );
document.write( "b = 6<BR>\n" );
document.write( "c = -27<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "b^2 = 36<BR>\n" );
document.write( "4*a*c = -108<BR>\n" );
document.write( "2*a = 2<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "quadratic formula becomes<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-6+%2B-+sqrt%2836-%28-108%29%29%29%2F2 ALIGN=MIDDLE  ALT=\"%28-6+%2B-+sqrt%2836-%28-108%29%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "this becomes:<BR>\n" );
document.write( "x = (-6 +/- 12)/2<BR>\n" );
document.write( "which becomes<BR>\n" );
document.write( "x = 6/2 = 3<BR>\n" );
document.write( "or:<BR>\n" );
document.write( "x = -18/2 = -9<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "the answers are the same.<BR>\n" );
document.write( "you could solve by completing the square or you could solve by quadratic formula, whichever is easiest for you.<BR>\n" );
document.write( "-----\r<BR>\n" );
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document.write( " </SPAN>\n" );
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