document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=59822>Question 59822</A>: <I><SPAN STYLE=\"word-break: break-all;\"> can you please help me with this word problem.  thank you very much\r<BR>\n" );
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document.write( "112. Swimming pool design. An architect has a designed a motel pool with in a rectangular area the is fenced on three sides.  If she uses 60 yards of fencing to enclose as area of 352 square yards, then what are the dimensions for L and W?  Assume L is greater than W </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #41071 by </B><A HREF=/tutors/aboutme.mpl?userid=joyofmath><B>joyofmath(189)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=joyofmath><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=41071\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let the width of the pool = W and the length of the pool = L. We are told that the length is greater than W so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L+%3E+W ALIGN=MIDDLE  ALT=\"L+%3E+W\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Assume the three sides that are fenced in are the two widths and one length, and that's with 60 yards of fencing. Thus, \r<BR>\n" );
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document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2W%2BL+=+60 ALIGN=MIDDLE  ALT=\"2W%2BL+=+60\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We also know that the area of the pool = 352. So, \r<BR>\n" );
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document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=LW+=+352 ALIGN=MIDDLE  ALT=\"LW+=+352\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2W ALIGN=MIDDLE  ALT=\"2W\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides of (1) to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L+=+60-2W ALIGN=MIDDLE  ALT=\"L+=+60-2W\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Replace L with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60-2W ALIGN=MIDDLE  ALT=\"60-2W\"   DISABLED_style= \"max-width:90%; height:auto;\" > in (2) to get \r<BR>\n" );
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document.write( "(3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2860-2W%29W+=+352 ALIGN=MIDDLE  ALT=\"%2860-2W%29W+=+352\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now, multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60-2W ALIGN=MIDDLE  ALT=\"60-2W\"   DISABLED_style= \"max-width:90%; height:auto;\" > by W and we get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60W-2W%5E2 ALIGN=MIDDLE  ALT=\"60W-2W%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. <BR>\n" );
document.write( "So, (3) becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60W-2W%5E2+=+352 ALIGN=MIDDLE  ALT=\"60W-2W%5E2+=+352\"   DISABLED_style= \"max-width:90%; height:auto;\" > or \r<BR>\n" );
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document.write( "(4) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60W-2W%5E2-352+=+0 ALIGN=MIDDLE  ALT=\"60W-2W%5E2-352+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This is a quadratic equation which can also be written as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2W%5E2%2B60W-352+=+0 ALIGN=MIDDLE  ALT=\"-2W%5E2%2B60W-352+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "We divide both sides by 2 and get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-W%5E2%2B30W-176+=+0 ALIGN=MIDDLE  ALT=\"-W%5E2%2B30W-176+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "The coefficients of this quadratic equation are -1, 30, and -176.\r<BR>\n" );
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document.write( "Remember the quadratic equation, solving for w: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W+=+%28-b+%2B-+sqrt%28b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"W+=+%28-b+%2B-+sqrt%28b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Replace a, b, and c with -1, 30, and -176 respectively and you get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W+=+%28-%2830%29+%2B-+sqrt%2830%5E2+-+4%2A%28-1%29%2A%28-176%29%29%29+%2F+%282%2A%28-1%29%29 ALIGN=MIDDLE  ALT=\"W+=+%28-%2830%29+%2B-+sqrt%2830%5E2+-+4%2A%28-1%29%2A%28-176%29%29%29+%2F+%282%2A%28-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Multiply things out and you get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W+=+%28-30+%2B-+sqrt%28900+-+704%29%29+%2F+-2 ALIGN=MIDDLE  ALT=\"W+=+%28-30+%2B-+sqrt%28900+-+704%29%29+%2F+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W+=+%28-30+%2B-+sqrt%28196%29%29+%2F+-2 ALIGN=MIDDLE  ALT=\"W+=+%28-30+%2B-+sqrt%28196%29%29+%2F+-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=sqrt%28196%29+=+14 ALIGN=MIDDLE  ALT=\"sqrt%28196%29+=+14\"   DISABLED_style= \"max-width:90%; height:auto;\" > so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W+=+%28-30+%2B-+14%29+%2F+-2 ALIGN=MIDDLE  ALT=\"W+=+%28-30+%2B-+14%29+%2F+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So, W can equal <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-30+%2B+14%29+%2F+-2 ALIGN=MIDDLE  ALT=\"%28-30+%2B+14%29+%2F+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > which = 8<BR>\n" );
document.write( "or W can equal <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-30+-+14+%29+%2F+-2 ALIGN=MIDDLE  ALT=\"%28-30+-+14+%29+%2F+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > which = 22\r<BR>\n" );
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document.write( "From (1) we know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2W%2BL+=+60 ALIGN=MIDDLE  ALT=\"2W%2BL+=+60\"   DISABLED_style= \"max-width:90%; height:auto;\" >. If W = 8 then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2AW%2BL+=+60 ALIGN=MIDDLE  ALT=\"2%2AW%2BL+=+60\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%2BL+=+60 ALIGN=MIDDLE  ALT=\"16%2BL+=+60\"   DISABLED_style= \"max-width:90%; height:auto;\" > so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L+=+44 ALIGN=MIDDLE  ALT=\"L+=+44\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "If W = 22 then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2AW%2BL+=+60 ALIGN=MIDDLE  ALT=\"2%2AW%2BL+=+60\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A22+%2B+L+=+60 ALIGN=MIDDLE  ALT=\"2%2A22+%2B+L+=+60\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=44%2BL+=+60 ALIGN=MIDDLE  ALT=\"44%2BL+=+60\"   DISABLED_style= \"max-width:90%; height:auto;\" > so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=16 ALIGN=MIDDLE  ALT=\"L=16\"   DISABLED_style= \"max-width:90%; height:auto;\" >. But, L must be > W and 16 is not > 22 so W = 22 is not a solution.\r<BR>\n" );
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document.write( "So, L = 44. and from (1) we know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2W%2BL+=+60 ALIGN=MIDDLE  ALT=\"2W%2BL+=+60\"   DISABLED_style= \"max-width:90%; height:auto;\" > so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2W%2B44+=+60 ALIGN=MIDDLE  ALT=\"2W%2B44+=+60\"   DISABLED_style= \"max-width:90%; height:auto;\" > so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2W+=+16 ALIGN=MIDDLE  ALT=\"2W+=+16\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W+=+8 ALIGN=MIDDLE  ALT=\"W+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "To verify our answer, that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L+=+44 ALIGN=MIDDLE  ALT=\"L+=+44\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W+=+8 ALIGN=MIDDLE  ALT=\"W+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" > we plug these values into (1) and (2):\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2W%2BL+=+60 ALIGN=MIDDLE  ALT=\"2W%2BL+=+60\"   DISABLED_style= \"max-width:90%; height:auto;\" > so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A8+%2B+44 ALIGN=MIDDLE  ALT=\"2%2A8+%2B+44\"   DISABLED_style= \"max-width:90%; height:auto;\" > should = 60 and it does.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=LW+=+352 ALIGN=MIDDLE  ALT=\"LW+=+352\"   DISABLED_style= \"max-width:90%; height:auto;\" > so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=44%2A8 ALIGN=MIDDLE  ALT=\"44%2A8\"   DISABLED_style= \"max-width:90%; height:auto;\" > should = 352 and it does. </SPAN>\n" );
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