document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=148258>Question 148258</A>: <I><SPAN STYLE=\"word-break: break-all;\"> John increased the area of his garden by 120 ft^2. The original garden was 12 ft. by 14 ft., and he increased the length and the width by the same amount. Find the exact dimensions of the new garden and approximate the dimensions in feet and inches. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #108657 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=108657\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x=amount he increased the dimensions of his garden, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bo%5D ALIGN=MIDDLE  ALT=\"A%5Bo%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >=area of original garden and  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bn%5D ALIGN=MIDDLE  ALT=\"A%5Bn%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >=area of new garden\r<BR>\n" );
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document.write( "Since the original garden is 12 ft by 14 ft, this means that the area of the original garden is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bo%5D=12%2A14=168 ALIGN=MIDDLE  ALT=\"A%5Bo%5D=12%2A14=168\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bo%5D=168 ALIGN=MIDDLE  ALT=\"A%5Bo%5D=168\"   DISABLED_style= \"max-width:90%; height:auto;\" > which means that the area of the original garden is 168 ft^2\r<BR>\n" );
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document.write( "Because the area of the new garden is 120 ft^2 larger than the original garden, this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bn%5D=A%5Bo%5D%2B120 ALIGN=MIDDLE  ALT=\"A%5Bn%5D=A%5Bo%5D%2B120\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bn%5D=168%2B120 ALIGN=MIDDLE  ALT=\"A%5Bn%5D=168%2B120\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bo%5D=168 ALIGN=MIDDLE  ALT=\"A%5Bo%5D=168\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bn%5D=288 ALIGN=MIDDLE  ALT=\"A%5Bn%5D=288\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add\r<BR>\n" );
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document.write( "So the area of the new garden is 288 ft^2\r<BR>\n" );
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document.write( "Now since he increased the dimensions by some unknown amount, this means that the area of the new garden is equal to:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bn%5D=%2812%2Bx%29%2814%2Bx%29 ALIGN=MIDDLE  ALT=\"A%5Bn%5D=%2812%2Bx%29%2814%2Bx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=288=%2812%2Bx%29%2814%2Bx%29 ALIGN=MIDDLE  ALT=\"288=%2812%2Bx%29%2814%2Bx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bn%5D=288 ALIGN=MIDDLE  ALT=\"A%5Bn%5D=288\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=288=168%2B26x%2Bx%5E2 ALIGN=MIDDLE  ALT=\"288=168%2B26x%2Bx%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > FOIL\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=168%2B26x%2Bx%5E2-288 ALIGN=MIDDLE  ALT=\"0=168%2B26x%2Bx%5E2-288\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 288 from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=x%5E2%2B26x-120 ALIGN=MIDDLE  ALT=\"0=x%5E2%2B26x-120\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine and rearrange the terms.\r<BR>\n" );
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document.write( "Let's use the quadratic formula to solve for x\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the quadratic formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-%2826%29+%2B-+sqrt%28+%2826%29%5E2-4%281%29%28-120%29+%29%29%2F%282%281%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-%2826%29+%2B-+sqrt%28+%2826%29%5E2-4%281%29%28-120%29+%29%29%2F%282%281%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1 ALIGN=MIDDLE  ALT=\"a=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=26 ALIGN=MIDDLE  ALT=\"b=26\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-120 ALIGN=MIDDLE  ALT=\"c=-120\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-26+%2B-+sqrt%28+676-4%281%29%28-120%29+%29%29%2F%282%281%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-26+%2B-+sqrt%28+676-4%281%29%28-120%29+%29%29%2F%282%281%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=26 ALIGN=MIDDLE  ALT=\"26\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=676 ALIGN=MIDDLE  ALT=\"676\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-26+%2B-+sqrt%28+676--480+%29%29%2F%282%281%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-26+%2B-+sqrt%28+676--480+%29%29%2F%282%281%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%281%29%28-120%29 ALIGN=MIDDLE  ALT=\"4%281%29%28-120%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-480 ALIGN=MIDDLE  ALT=\"-480\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-26+%2B-+sqrt%28+676%2B480+%29%29%2F%282%281%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-26+%2B-+sqrt%28+676%2B480+%29%29%2F%282%281%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28676--480%29 ALIGN=MIDDLE  ALT=\"sqrt%28676--480%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28676%2B480%29 ALIGN=MIDDLE  ALT=\"sqrt%28676%2B480%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-26+%2B-+sqrt%28+1156+%29%29%2F%282%281%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-26+%2B-+sqrt%28+1156+%29%29%2F%282%281%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=676 ALIGN=MIDDLE  ALT=\"676\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=480 ALIGN=MIDDLE  ALT=\"480\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1156 ALIGN=MIDDLE  ALT=\"1156\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-26+%2B-+sqrt%28+1156+%29%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=+%28-26+%2B-+sqrt%28+1156+%29%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-26+%2B-+34%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=+%28-26+%2B-+34%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1156 ALIGN=MIDDLE  ALT=\"1156\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=34 ALIGN=MIDDLE  ALT=\"34\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-26+%2B+34%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=+%28-26+%2B+34%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-26+-+34%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=+%28-26+-+34%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the expression. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%288%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=+%288%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=++%28-60%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=++%28-60%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+4 ALIGN=MIDDLE  ALT=\"x+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-30 ALIGN=MIDDLE  ALT=\"x+=+-30\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify. \r<BR>\n" );
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document.write( "So the possible answers are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+4 ALIGN=MIDDLE  ALT=\"x+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-30 ALIGN=MIDDLE  ALT=\"x+=+-30\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "  \r<BR>\n" );
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document.write( "However, since a negative length is not possible, this means that he increased his garden by 4 feet.\r<BR>\n" );
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document.write( "Now simply add 4 to each dimension 12 and 14 to get:\r<BR>\n" );
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document.write( "12+4=16  by 14+4=18\r<BR>\n" );
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document.write( "So the dimensions of the new garden are\r<BR>\n" );
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document.write( "16 ft by 18 ft\r<BR>\n" );
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document.write( "note: the approximate answers are the same as the exact answers since there are no square roots, fractions, decimals, etc. in the answer\r<BR>\n" );
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document.write( " </SPAN>\n" );
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