document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=263662>Question 263662</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A rectangular piece of sheet metal is 3 in. longer than it is wide.  If the length and width are both increased by 2 in. the area increases by 34 in squared.  What are the original dimensions of the sheet metal? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #194296 by </B><A HREF=/tutors/aboutme.mpl?userid=oberobic><B>oberobic(2304)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=oberobic><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=194296\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given what we know about rectangles...<BR>\n" );
document.write( "A = area = l * w <BR>\n" );
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document.write( "We are told:  l = w+3<BR>\n" );
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document.write( "If we set l+2 and w+2  (that is we increase both by 2), then area = A + 34 sq in.<BR>\n" );
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document.write( "We need to define everything in terms of one term.<BR>\n" );
document.write( "l = w+3<BR>\n" );
document.write( "So<BR>\n" );
document.write( "l+2 = w+5<BR>\n" );
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document.write( "That means:<BR>\n" );
document.write( "Original Area = w(w+3)<BR>\n" );
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document.write( "And the new area is:  (w+2)(w+5).<BR>\n" );
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document.write( "Combining the facts we have at hand:<BR>\n" );
document.write( "w(w+3) + 34 = (w+2)(w+5)<BR>\n" );
document.write( "w^2 + 3w + 34 = w^2 + 7w + 10<BR>\n" );
document.write( "Subtracting w^2 from both sides<BR>\n" );
document.write( "3w + 34 = 7w + 10<BR>\n" );
document.write( "Subtracting 10 from both sides<BR>\n" );
document.write( "3w + 24 = 7w<BR>\n" );
document.write( "Subtracting 3w from both sides<BR>\n" );
document.write( "24 = 4w<BR>\n" );
document.write( "4w = 24<BR>\n" );
document.write( "w = 6<BR>\n" );
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document.write( "Recall 'w' is the original width.  The length 'l' = w+3, so it is 9.<BR>\n" );
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document.write( "We need to check our work by comparing the areas to see if they are different by 34.<BR>\n" );
document.write( "A = 6*9 = 54<BR>\n" );
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document.write( "The new dimensions are:  8 & 11<BR>\n" );
document.write( "New Area = 8*11 = 88<BR>\n" );
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document.write( "54+34 = 88.  OK<BR>\n" );
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document.write( "Answer:  The original dimensions of the sheet of metal are 6 by 9 inches. </SPAN>\n" );
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