document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=698534>Question 698534</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Lady Greenthumb has a rectangular garden that measures 12m by 5m. Since it is still possible for her to extend her garden, she cultivated a uniform width of land around the garden, thereby doubling the area. Find the dimensions of the new garden. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #430792 by </B><A HREF=/tutors/aboutme.mpl?userid=Simnepi><B>Simnepi(216)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Simnepi><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=Simnepi><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=430792\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> putting a border around the garden increases each dimension by twice the width of the border. (Draw a sketch!)<BR>\n" );
document.write( "Let the width of this border be called x.<BR>\n" );
document.write( "The new dimensions of the garden are 12+2x and 5+2x.<BR>\n" );
document.write( "The area is doubled (The original area is 12m X 5m = 60m^2)  so we can write an equation to find the new area thus..<BR>\n" );
document.write( "(12+2x)(5+2x) = 120<BR>\n" );
document.write( "Expanding the bracket and simplifying gives<BR>\n" );
document.write( "60 + 34x + 4x^2 = 120<BR>\n" );
document.write( "divide by 2 throughout (to make the numbers smaller) giving<BR>\n" );
document.write( "30 + 17x + 2x^2 = 60<BR>\n" );
document.write( "rearranging this we get<BR>\n" );
document.write( "2x^2 + 17x - 30 = 0<BR>\n" );
document.write( "Now we have to factorize<BR>\n" );
document.write( "Find factors of -30 (the constant term) i.e. (plus/minus) 2 and 15, 3 and 10, 5 and 6<BR>\n" );
document.write( "We also have to consider the coefficient of the x^2 term (which is 2!)<BR>\n" );
document.write( "now we try to make +17 (the coefficient of the x term) using the factor pairs and the 2 from the x^2 term<BR>\n" );
document.write( "By trial and error we find that 2 X 10 and -3 can make +17. thus we get<BR>\n" );
document.write( "(2x-3)(x+10) = 0<BR>\n" );
document.write( "thus either (x+10) = 0 or (2x-3) = 0<BR>\n" );
document.write( "if (x=10)=0 then x = -10 (a negative measurement is nonsense)<BR>\n" );
document.write( "so (2x-3)=0<BR>\n" );
document.write( "therefore 2x = 3<BR>\n" );
document.write( "so x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F2 ALIGN=MIDDLE  ALT=\"3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > m (1.5m)\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );