document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=213072>Question 213072</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a rectangle is 5 ft longer than its width. if the lenght is shortened by 2 ft and the width is increased by 1 ft, the area remains unchanged. find the area. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #160974 by </B><A HREF=/tutors/aboutme.mpl?userid=aggie_tutor><B>aggie_tutor(13)</B></A><img src=\"/images/stars/stars-06.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=aggie_tutor><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=aggie_tutor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=160974\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> They trick you a little: They are asking for the area, but first you have to solve for the actual width. Fortunately this works out pretty easily. Let width above be w and rectangles A and B.\r<BR>\n" );
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document.write( "Area of rectangle A: <BR>\n" );
document.write( "Width = w<BR>\n" );
document.write( "Length = w + 5<BR>\n" );
document.write( "Area rectangle A: (Length * Widgth) AreaA = (w)*(w+5)\r<BR>\n" );
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document.write( "Area of rectangle B:<BR>\n" );
document.write( "Width = w + 1<BR>\n" );
document.write( "Length = (w + 5) - 2<BR>\n" );
document.write( "Area rectangel B: (Length * Width) AreaB = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28w%2B1%29%2A%28w%2B5-2%29+=+%28w%2B1%29%2A%28w%2B3%29 ALIGN=MIDDLE  ALT=\"%28w%2B1%29%2A%28w%2B5-2%29+=+%28w%2B1%29%2A%28w%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now the problem says the two areas are equal. Set each area computation equal to the other, and solve for width w. \r<BR>\n" );
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document.write( "AreaA = AreaB<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28w%29%2A%28w%2B5%29+=+%28w%2B1%29%2A%28w%2B3%29 ALIGN=MIDDLE  ALT=\"%28w%29%2A%28w%2B5%29+=+%28w%2B1%29%2A%28w%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Simplify with distributive property:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28w%2Aw%29+%2B+%285%2Aw%29+=+%28w%2Aw%29+%2B+%281%2A3%29+%2B+%283%2Aw%29+%2B+%281%2Aw%29 ALIGN=MIDDLE  ALT=\"%28w%2Aw%29+%2B+%285%2Aw%29+=+%28w%2Aw%29+%2B+%281%2A3%29+%2B+%283%2Aw%29+%2B+%281%2Aw%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Combine like terms.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%5E2+%2B+5w+=+w%5E2+%2B+3+%2B+%283w+%2B+w%29 ALIGN=MIDDLE  ALT=\"w%5E2+%2B+5w+=+w%5E2+%2B+3+%2B+%283w+%2B+w%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%5E2+%2B+5w+=+w%5E2+%2B+3+%2B+4w ALIGN=MIDDLE  ALT=\"w%5E2+%2B+5w+=+w%5E2+%2B+3+%2B+4w\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Subtrace the w^2 from each side to get rid of it. The square term cancels itself out, which is really convenient so we don't have to take a root of anything (!).<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%5E2+%2B+5w+%28-w%5E2%29+=+w%5E2+%2B+3+%2B+4w+%28-w%5E2%29 ALIGN=MIDDLE  ALT=\"w%5E2+%2B+5w+%28-w%5E2%29+=+w%5E2+%2B+3+%2B+4w+%28-w%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5w+=+3+%2B+4w ALIGN=MIDDLE  ALT=\"5w+=+3+%2B+4w\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Subtract 4w from both sides to isolate the number 3.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5w+-+4w+=+3+%2B+4w+%28-+4w%29 ALIGN=MIDDLE  ALT=\"5w+-+4w+=+3+%2B+4w+%28-+4w%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5w+-+4w+=+3 ALIGN=MIDDLE  ALT=\"5w+-+4w+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w+=+3 ALIGN=MIDDLE  ALT=\"w+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Then plug in w to one of the rectangles to get the area. <BR>\n" );
document.write( "AreaA = Length * Width = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w+%2A+%28w%2B5%29+=+3+%2A+%283%2B5%29+=+3%2A8+=+24 ALIGN=MIDDLE  ALT=\"w+%2A+%28w%2B5%29+=+3+%2A+%283%2B5%29+=+3%2A8+=+24\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Check your answer by subbing w in the other rectangle:<BR>\n" );
document.write( "AreaB = Length * Width = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28w%2B5-2%29+%2A+%28w%2B1%29+=+%283%2B5-2%29+%2A+%283%2B1%29+=+6%2A4+=+24 ALIGN=MIDDLE  ALT=\"%28w%2B5-2%29+%2A+%28w%2B1%29+=+%283%2B5-2%29+%2A+%283%2B1%29+=+6%2A4+=+24\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "AreaA = AreaB !  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );