document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1194689>Question 1194689</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Mr. Garcia owns an irregular field that is in the shape of two squares, side by side. The area of the field is 17,396 yd2, and the perimeter is 572 yd. What is the length of the longest side of the field? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #826944 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=826944\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Edit: Disregard my answer below. The tutor greenestamps makes a good point that the squares are very likely of different sizes, which I didn't consider. My apologies.\r<BR>\n" );
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document.write( "It sounds like this field is a rectangle, since the two squares are joined side by side (I'm assuming on the same horizontal level).<BR>\n" );
document.write( "I don't know why your teacher considers a rectangle to be irregular, unless s/he means \"the figure isn't a regular polygon\".\r<BR>\n" );
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document.write( "Regular polygon = it has all sides equal, and all angles equal<BR>\n" );
document.write( "Examples: <ul><li>an equilateral triangle is a regular polygon with 3 equal sides. All angles are 60 degrees.</li><li>any square is a four sided regular polygon. All four sides are equal, and all four angles are equal to 90 degrees.</li></ul>Anyways, onto the problem at hand.\r<BR>\n" );
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document.write( "L = length = longer side<BR>\n" );
document.write( "W = width = shorter side<BR>\n" );
document.write( "These are positive real numbers.\r<BR>\n" );
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document.write( "P = perimeter of a rectangle<BR>\n" );
document.write( "P = 2(L+W)\r<BR>\n" );
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document.write( "Plug in the given perimeter P = 572 and solve for L<BR>\n" );
document.write( "P = 2(L+W)<BR>\n" );
document.write( "572 = 2(L+W)<BR>\n" );
document.write( "L+W = 572/2<BR>\n" );
document.write( "L+W = 286<BR>\n" );
document.write( "L = 286-W\r<BR>\n" );
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document.write( "A = area of the rectangle<BR>\n" );
document.write( "A = length*width<BR>\n" );
document.write( "A = L*W<BR>\n" );
document.write( "A = (286-W)*W\r<BR>\n" );
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document.write( "Plug in the given area A = 17396 and rearrange terms like so<BR>\n" );
document.write( "The goal from here is to solve for W.<BR>\n" );
document.write( "A = (286-W)*W<BR>\n" );
document.write( "17396 = (286-W)*W<BR>\n" );
document.write( "17396 = 286W-W^2<BR>\n" );
document.write( "W^2-286W+17396 = 0\r<BR>\n" );
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document.write( "This may be able to be factored, but the trial and error process is quite frankly annoying. It may turn out that this cannot be factored at all.\r<BR>\n" );
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document.write( "I prefer the quadratic formula instead.<BR>\n" );
document.write( "It is more direct and to the point. <BR>\n" );
document.write( "No guess-and-check is required, and it works for any quadratic.\r<BR>\n" );
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document.write( "Plug in a = 1, b = -286, c = 17396<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"W+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%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=W+=+%28-%28-286%29%2B-sqrt%28%28-286%29%5E2-4%281%29%2817396%29%29%29%2F%282%281%29%29 ALIGN=MIDDLE  ALT=\"W+=+%28-%28-286%29%2B-sqrt%28%28-286%29%5E2-4%281%29%2817396%29%29%29%2F%282%281%29%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=W+=+%28286%2B-sqrt%2881796+-+69584%29%29%2F%282%29 ALIGN=MIDDLE  ALT=\"W+=+%28286%2B-sqrt%2881796+-+69584%29%29%2F%282%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=W+=+%28286%2B-sqrt%2812212%29%29%2F%282%29 ALIGN=MIDDLE  ALT=\"W+=+%28286%2B-sqrt%2812212%29%29%2F%282%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=W+=+%28286%2B-++110.507918%29%2F%282%29 ALIGN=MIDDLE  ALT=\"W+=+%28286%2B-++110.507918%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is approximate\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W+=+%28286%2B110.507918%29%2F%282%29 ALIGN=MIDDLE  ALT=\"W+=+%28286%2B110.507918%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W+=+%28286-110.507918%29%2F%282%29 ALIGN=MIDDLE  ALT=\"W+=+%28286-110.507918%29%2F%282%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=W+=+%28396.507918%29%2F%282%29 ALIGN=MIDDLE  ALT=\"W+=+%28396.507918%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W+=+%28175.492082%29%2F%282%29 ALIGN=MIDDLE  ALT=\"W+=+%28175.492082%29%2F%282%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=W+=+198.253959 ALIGN=MIDDLE  ALT=\"W+=+198.253959\"   DISABLED_style= \"max-width:90%; height:auto;\" > or  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W+=+87.746041 ALIGN=MIDDLE  ALT=\"W+=+87.746041\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The decimal values are approximate.\r<BR>\n" );
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document.write( "If W = 198.253959, then,<BR>\n" );
document.write( "L = 286-W = 286-198.253959 = 87.746041\r<BR>\n" );
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document.write( "Then notice how<BR>\n" );
document.write( "area = L*W = 87.746041*198.253959 = 17,396.0000148263<BR>\n" );
document.write( "which is fairly close to the target area of 17,396.<BR>\n" );
document.write( "This helps confirm the answer.<BR>\n" );
document.write( "Use more precision in the quadratic formula steps to get a more accurate value for W, which in turn leads to a more accurate value for L.\r<BR>\n" );
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document.write( "You should find that if W = 87.746041, then it leads to L = 198.253959\r<BR>\n" );
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document.write( "Answer: The longest side is roughly equal to 198.253959 yards.<BR>\n" );
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