document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=171289>Question 171289</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need your help on the following word problem:<BR>\n" );
document.write( "A rectangle is 15cm wide and 18cm long. If both dimensions are decreased by the same amount, the area of the new rectangle is 116cm squared less than the area of the original. Find the dimensions of the new rectangle.<BR>\n" );
document.write( "Thank You </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #126449 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=126449\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> width of rectangle equals 15 centimeters.<BR>\n" );
document.write( "length of rectangle equals 18 centimeters.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "let L = length<BR>\n" );
document.write( "let W = width<BR>\n" );
document.write( "let A = area.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "area of triangle = length times width:<BR>\n" );
document.write( "A = L * W<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "If both dimensions are decreased by the same amount, the area of the new rectangle is 116cm squared less than the area of the original.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "let x be the amount the length and the width are decreased by.<BR>\n" );
document.write( "your formula to solve would be:<BR>\n" );
document.write( "A - 116 = (L-x) * (W-x)<BR>\n" );
document.write( "since A is the original area and it is equal to L * W, you can substitute in the equation to get:<BR>\n" );
document.write( "(L*W) - 116 = (L-x)*(W-x)<BR>\n" );
document.write( "since you know what L is and you know what W is you can substitute for them in the equation:<BR>\n" );
document.write( "(18*15) - 116 = (18-x)*(15-x)<BR>\n" );
document.write( "simplify:<BR>\n" );
document.write( "270 - 116 = 270 - 18*x - 15*x + x^2<BR>\n" );
document.write( "subtract 270 from both sides and it simplify further:<BR>\n" );
document.write( "- 116 = -33*x + x^2<BR>\n" );
document.write( "add 116 to both sides and rearrange to the standard order exponents (highest order first):<BR>\n" );
document.write( "x^2 - 33*x + 116 = 0<BR>\n" );
document.write( "solve the quadratic equation of:<BR>\n" );
document.write( "x^2 - 33*x + 116 = 0<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "i didn't see it right away, so i used the quadratic formula of:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28%28-b%29%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"x+=+%28%28-b%29%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "to solve the quadratic equation.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "the standard form of the quadratic equation is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Ax%5E2+%2B+b%2Ax+%2B+c+=+0 ALIGN=MIDDLE  ALT=\"a%2Ax%5E2+%2B+b%2Ax+%2B+c+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a is the coefficient of x^2<BR>\n" );
document.write( "b is the coefficient of x<BR>\n" );
document.write( "c is the constant term<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "in your equation,<BR>\n" );
document.write( "a = 1<BR>\n" );
document.write( "b = -33<BR>\n" );
document.write( "c = 116<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "the factors came out to be:<BR>\n" );
document.write( "(x-29) * (x-4) = 0<BR>\n" );
document.write( "x = 29<BR>\n" );
document.write( "or:<BR>\n" );
document.write( "x = 4<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "to see which of these answers is correct, we need to substitute them in the original equation.<BR>\n" );
document.write( "----- <BR>\n" );
document.write( "the original equation is:<BR>\n" );
document.write( "(18*15) - 116 = (18-x)*(15-x)<BR>\n" );
document.write( "substitute 29 for x:<BR>\n" );
document.write( "(18*15) - 116 = (18-29)*(15-29)<BR>\n" );
document.write( "simplify:<BR>\n" );
document.write( "270 - 116 = (-11)*(-14)<BR>\n" );
document.write( "154 = 154<BR>\n" );
document.write( "x = 29 works.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "substitute 4 for x:<BR>\n" );
document.write( "(18*15) - 116 = (18-4)*(15-4)<BR>\n" );
document.write( "simplify:<BR>\n" );
document.write( "270 - 116 = (14)*(11)<BR>\n" );
document.write( "154 = 154<BR>\n" );
document.write( "x = 4 works as well.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "your answer is <BR>\n" );
document.write( "x = 4 centimeters<BR>\n" );
document.write( "or<BR>\n" );
document.write( "x = 29 centimeters<BR>\n" );
document.write( "-----<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );