document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=186249>Question 186249</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A rectangle is 4 times as long as it is wide. a second rectangle is 5 cm longer and 2 cm wider than the first. the are of the second rectangle is 270 square cm greater than the first. What are the dimensions of the original rectangle?          <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #139700 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=139700\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A rectangle is 4 times as long as it is wide. a second rectangle is 5 cm longer and 2 cm wider than the first. the are of the second rectangle is 270 square cm greater than the first. What are the dimensions of the original rectangle?<BR>\n" );
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document.write( "Let x = width of the 1st rectangle:<BR>\n" );
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document.write( "\"A rectangle is 4 times as long as it is wide.\"<BR>\n" );
document.write( "4x = length of the 1st rectangle<BR>\n" );
document.write( "then<BR>\n" );
document.write( "4x^2 sq/cm = area of 1st rectangle<BR>\n" );
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document.write( "a second rectangle is 5 cm longer and 2 cm wider than the first.\"<BR>\n" );
document.write( "(4x + 5) = length of 2nd rectangle<BR>\n" );
document.write( "(x + 2) = width of 2nd rectangle<BR>\n" );
document.write( "then find the area of the 2nd rectangle<BR>\n" );
document.write( "FOIL:(4x+5)*(x+2) = 4x^2 + 8x + 5x + 10 = 4x^2 + 13x + 10 sq cm<BR>\n" );
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document.write( "the area of the second rectangle is 270 square cm greater than the first.<BR>\n" );
document.write( "4x^2 + 13x + 10 - 4x^2 = 270<BR>\n" );
document.write( "4x^2 - 4x^2 + 13x = 270 - 10<BR>\n" );
document.write( "13x = 260<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=260%2F13 ALIGN=MIDDLE  ALT=\"260%2F13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = 20 <BR>\n" );
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document.write( " What are the dimensions of the original rectangle?<BR>\n" );
document.write( "4(20) = 80 cm is the length <BR>\n" );
document.write( "80 by 20 is the dimensions of the original rectangle<BR>\n" );
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document.write( "Check solution, find the area of both rectangles<BR>\n" );
document.write( "4(20) + 5 = 85 cm<BR>\n" );
document.write( "20 + 2 = 22 cm<BR>\n" );
document.write( "85 * 22 = 1870 sq cm area of 2nd rectangle<BR>\n" );
document.write( "and<BR>\n" );
document.write( "80 * 20 = 1600 sq cm area of 1st rectangle<BR>\n" );
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document.write( "1870 - 1600 = 270 confirms our solution<BR>\n" );
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