document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=170636>Question 170636</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0618044302/algebrahomeworkh>Algebra structure and method book one</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Originally the dimensions of a rectangle were 20 cm by 23 cm. When both dimensions were decreased by the same amount, the area of the rectangle decreased by 120 cm^2. Find the dimensions of the new rectangle. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #125964 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=125964\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Originally the dimensions of a rectangle were 20 cm by 23 cm. When both dimensions were decreased by the same amount, the area of the rectangle decreased by 120 cm^2. Find the dimensions of the new rectangle.<BR>\n" );
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document.write( "Original DATA:<BR>\n" );
document.write( "area = 20*23 = 460 cm^2<BR>\n" );
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document.write( "New DATA:<BR>\n" );
document.write( "area = (20-x)(23-x) cm^2<BR>\n" );
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document.write( "EQUATION:<BR>\n" );
document.write( "original area - new area = 120 cm^2<BR>\n" );
document.write( "460 -[460-43x+x^2] = 120<BR>\n" );
document.write( "460 - 460 +43x - x^2 = 120<BR>\n" );
document.write( "x^2 - 43x + 120 = 0\r<BR>\n" );
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document.write( "x = [43 +- sqrt(43^2 -4*120)}/2\r<BR>\n" );
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document.write( "x = [43 +- sqrt(1369)]/2\r<BR>\n" );
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document.write( "x = [43 +- 37]/2<BR>\n" );
document.write( "Positive solution:\r<BR>\n" );
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document.write( "x = 3 cm or x = 40 cm<BR>\n" );
document.write( "Only x = 3 cm is realistic.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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