document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=104690>Question 104690</A>: <I><SPAN STYLE=\"word-break: break-all;\"> use factoring to solve problem\r<BR>\n" );
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document.write( "a triangular sail has an area of x^2 + 5x + 6 square meters and a height of x + 3 meters. find the lenght of the sails base </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #76209 by </B><A HREF=/tutors/aboutme.mpl?userid=TP><B>TP(29)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=TP><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=76209\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To do this you need to remember that<BR>\n" );
document.write( "Area of triangle=(base*height)/2 and you should be able to factorise a quadratic trinomial expression such as ax^2+bx+c where a,b and c are given numbers(constants).You will need to be able to factorise x^2+5x+6.\r<BR>\n" );
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document.write( "Let the base be b metres(this is how we spell this word in \"English\" English).\r<BR>\n" );
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document.write( "Then Area of Triangle = [b*height]/2<BR>\n" );
document.write( "Since the height is given as (x+3) metres then<BR>\n" );
document.write( "Area=[b*(x+3)]/2.\r<BR>\n" );
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document.write( "But you are told that the area is x^2+5x+6<BR>\n" );
document.write( "So [b*(x+3)]/2 is the same as x^2+5x+6<BR>\n" );
document.write( "And so we can write<BR>\n" );
document.write( "[b*(x+3)]/2=x^2+5x+6<BR>\n" );
document.write( "Now the Left Hand Side of the equal sign is in a factorised form ,that is it is written as one thing times another thing (b times (x+3))<BR>\n" );
document.write( "So to be able to find out what b is we need to factorise the Right Hand Side which is x^2+5x+6.<BR>\n" );
document.write( "Suppose the factors are x+a and x+b then (x+a)*(x+b) =x^2 +(a+b)x+ab [Multiplying the brackets together]<BR>\n" );
document.write( "Now compare x^2+(a+b)x+ab (i) to x^2+5x+6 (ii).<BR>\n" );
document.write( "You can see that a+b in expression (i) is in the same place as the number 5 is in expression (ii)<BR>\n" );
document.write( " and where the ab is in (i) we have the number 6 in (ii)<BR>\n" );
document.write( "And so we can write<BR>\n" );
document.write( "a+b=5 and<BR>\n" );
document.write( "a*b=6 [this is called comparing coefficients]\r<BR>\n" );
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document.write( "So to be able to write x^2+5x+6 as (x+a)*(x+b) we need to find two numbers (a and b) so that when you add them together you get 5 and when you multiply them together you get 6.<BR>\n" );
document.write( "The numbers are then a=3 and b=2 (3+2=5 and 3*2=6)\r<BR>\n" );
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document.write( "This means then that we can write the equation [b*(x+3)]/2=x^2+5x+6 as\r<BR>\n" );
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document.write( "[b*(x+3)]/2=(x+3)*(x+2)<BR>\n" );
document.write( "Now share both sides by(x+3) and we get<BR>\n" );
document.write( "b/2=(x+2)<BR>\n" );
document.write( "Now multiply both sides by 2 and we get<BR>\n" );
document.write( "b=2*(x+2)<BR>\n" );
document.write( "Now multiply the bracket out(multiply everything in the bracket by 2) and we get<BR>\n" );
document.write( "b=2x+4<BR>\n" );
document.write( "And so the base is 2x+4 metres ANS </SPAN>\n" );
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