document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=484352>Question 484352</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do you solve this? \r<BR>\n" );
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document.write( "The dimensions of a rectangle are such that its length is 3 inches more than its width. If length were doubled and width decreased by 1, area would be increased by 176 inches squared. What are the length and width? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #331401 by </B><A HREF=/tutors/aboutme.mpl?userid=htmentor><B>htmentor(1343)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=htmentor><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=htmentor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=331401\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The dimensions of a rectangle are such that its length is 3 inches more than its width. If length were doubled and width decreased by 1, area would be increased by 176 inches squared. What are the length and width?<BR>\n" );
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document.write( "Given: l = w + 3 [1]<BR>\n" );
document.write( "The original area = A = lw<BR>\n" );
document.write( "For the new area we can write<BR>\n" );
document.write( "2l*(w-1) = A + 176<BR>\n" );
document.write( "2(w+3)*(w-1) = A + 176<BR>\n" );
document.write( "Substitute the value for l in [1] into the expressions for the two areas:<BR>\n" );
document.write( "A = w(w+3) [2]<BR>\n" );
document.write( "A + 176 = 2(w+3)(w-1) -> A = 2(w+3)(w-1) - 176<BR>\n" );
document.write( "Since the LHS's are equal, we can equate the RHS's:<BR>\n" );
document.write( "w(w+3) = 2(w+3)(w-1) - 176<BR>\n" );
document.write( "Simplify and solve for w:<BR>\n" );
document.write( "w^2 + 3w = 2w^2 + 4w - 6 - 176<BR>\n" );
document.write( "w^2 + w - 182 = 0<BR>\n" );
document.write( "w = (-1 +/- sqrt(1 + 4*182))/2<BR>\n" );
document.write( "w = (-1 +/- 27)/2 <BR>\n" );
document.write( "Taking the positive solution, we have w = 13<BR>\n" );
document.write( "Therefore l = 13 + 3 = 16<BR>\n" );
document.write( "Ans: w = 13, l = 16 </SPAN>\n" );
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