document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1171867>Question 1171867</A>: <I><SPAN STYLE=\"word-break: break-all;\"> To greet the 2020 SHS Graduates, a tarpaulin is to be set up along the national highway.If the area of the tarp is to be 35/4 m^2 and its perimeter is 27/2 meters, what should be the dimensions of the tarpaulin? Please help me answer this question. Arigathanks in advance.<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 #796783 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=796783\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "35/4 = 8.75<BR>\n" );
document.write( "27/2 = 13.5\r<BR>\n" );
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document.write( "The area is 8.75 square meters and the perimeter is 13.5 meters.\r<BR>\n" );
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document.write( "Let L and W be the length and width<BR>\n" );
document.write( "If the area is 8.75 square meters, then<BR>\n" );
document.write( "A = L*W<BR>\n" );
document.write( "L*W = A<BR>\n" );
document.write( "L*W = 8.75\r<BR>\n" );
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document.write( "If the perimeter is 13.5 meters, then<BR>\n" );
document.write( "P = 2*(L+W)<BR>\n" );
document.write( "2*(L+W) = 13.5<BR>\n" );
document.write( "L+W = 13.5/2<BR>\n" );
document.write( "L+W = 6.75<BR>\n" );
document.write( "L = 6.75-W\r<BR>\n" );
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document.write( "Plug this into the first equation and get everything to one side<BR>\n" );
document.write( "L*W = 8.75<BR>\n" );
document.write( "(6.75-W)*W = 8.75<BR>\n" );
document.write( "6.75W-W^2 = 8.75<BR>\n" );
document.write( "6.75W-W^2-8.75 = 0<BR>\n" );
document.write( "-W^2+6.75W-8.75 = 0<BR>\n" );
document.write( "100W^2-675W+875 = 0<BR>\n" );
document.write( "In the last step I multiplied both sides by -100 to clear out the decimals and to make the leading term positive.\r<BR>\n" );
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document.write( "From here we could divide every term by 25 going from<BR>\n" );
document.write( "100W^2-675W+875 = 0<BR>\n" );
document.write( "to<BR>\n" );
document.write( "4W^2-27W+35 = 0\r<BR>\n" );
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document.write( "Solving that equation is the same as solving <BR>\n" );
document.write( "4x^2-27x+35 = 0\r<BR>\n" );
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document.write( "Let's use the quadratic formula to solve\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b%2Bsqrt%28b%5E2-4ac%29%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"x+=+%28-b%2Bsqrt%28b%5E2-4ac%29%29%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b-sqrt%28b%5E2-4ac%29%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"x+=+%28-b-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=x+=+%28-%28-27%29%2Bsqrt%28%28-27%29%5E2-4%284%29%2835%29%29%29%2F%282%284%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-%28-27%29%2Bsqrt%28%28-27%29%5E2-4%284%29%2835%29%29%29%2F%282%284%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-%28-27%29-sqrt%28%28-27%29%5E2-4%284%29%2835%29%29%29%2F%282%284%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-%28-27%29-sqrt%28%28-27%29%5E2-4%284%29%2835%29%29%29%2F%282%284%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=x+=+%2827%2Bsqrt%28169%29%29%2F%288%29 ALIGN=MIDDLE  ALT=\"x+=+%2827%2Bsqrt%28169%29%29%2F%288%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2827-sqrt%28169%29%29%2F%288%29 ALIGN=MIDDLE  ALT=\"x+=+%2827-sqrt%28169%29%29%2F%288%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+=+%2827%2B13%29%2F%288%29 ALIGN=MIDDLE  ALT=\"x+=+%2827%2B13%29%2F%288%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2827-13%29%2F%288%29 ALIGN=MIDDLE  ALT=\"x+=+%2827-13%29%2F%288%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+=+%2840%29%2F%288%29 ALIGN=MIDDLE  ALT=\"x+=+%2840%29%2F%288%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2814%29%2F%288%29 ALIGN=MIDDLE  ALT=\"x+=+%2814%29%2F%288%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+=+5 ALIGN=MIDDLE  ALT=\"x+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+1.75 ALIGN=MIDDLE  ALT=\"x+=+1.75\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the width is either W = 5 or W = 1.75\r<BR>\n" );
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document.write( "If the width was W = 5, then,<BR>\n" );
document.write( "L = 6.75-W<BR>\n" );
document.write( "L = 6.75-5<BR>\n" );
document.write( "L = 1.75\r<BR>\n" );
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document.write( "Then note how<BR>\n" );
document.write( "L*W = 1.75*5 = 8.75<BR>\n" );
document.write( "and<BR>\n" );
document.write( "2*(L+W) = 2*(1.75+5) = 13.5<BR>\n" );
document.write( "which matches with our area and perimeter requirements. \r<BR>\n" );
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document.write( "So one possible set of dimensions is<BR>\n" );
document.write( "width = 5 meters<BR>\n" );
document.write( "length = 1.75 meters\r<BR>\n" );
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document.write( "If the width was W = 1.75, then,<BR>\n" );
document.write( "L = 6.75-W<BR>\n" );
document.write( "L = 6.75-1.75<BR>\n" );
document.write( "L = 5<BR>\n" );
document.write( "We basically get the flip of the previous section. So the order of the length and width doesn't matter.\r<BR>\n" );
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document.write( "We could say either<BR>\n" );
document.write( "length = 5 meters<BR>\n" );
document.write( "width = 1.75 meters<BR>\n" );
document.write( "OR<BR>\n" );
document.write( "length = 1.75 meters<BR>\n" );
document.write( "width = 5 meters\r<BR>\n" );
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document.write( "Regardless of the order, they will both satisfy the equations we set up earlier, so they fit the requirements your teacher has set.\r<BR>\n" );
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document.write( "In reality we only have one unique set of dimensions.\r<BR>\n" );
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document.write( "Answer: The rectangle is 5 meters by 1.75 meters<BR>\n" );
document.write( "Note: In fraction form, 1.75 = 7/4<BR>\n" );
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