document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=155442>Question 155442</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am having some trouble with this word problem, can some one help out and also show me the steps, thanks a lot\r<BR>\n" );
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document.write( "Hazel has a screen door whose height is 4 feet more than its width. She wishes to stabilize the door by attaching a steel cable diagonally. If the cable measures (Sqrt 194)/2 ft, what are the dimensions of the door? <BR>\n" );
document.write( "A) 2 1/4 ft by 6 1/4 ft<BR>\n" );
document.write( "B) 2 1/2 ft by 6 1/2 ft<BR>\n" );
document.write( "C) 3 ft by 7 ft<BR>\n" );
document.write( "D) 3 1/2 ft by 7 1/2 ft </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #114479 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=114479\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x = width \r<BR>\n" );
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document.write( "Since the \"height is 4 feet more than its width\", this means that the height is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B4 ALIGN=MIDDLE  ALT=\"x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > feet.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2Bb%5E2=c%5E2 ALIGN=MIDDLE  ALT=\"a%5E2%2Bb%5E2=c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with Pythagoreans Theorem. Note: \"a\" and \"b\" are the legs of the triangle (in this case the width and height of the door) and \"c\" is the hypotenuse (which in this problem is the diagonal of the door)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B%28x%2B4%29%5E2=%28sqrt%28194%29%2F2%29%5E2 ALIGN=MIDDLE  ALT=\"x%5E2%2B%28x%2B4%29%5E2=%28sqrt%28194%29%2F2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=x ALIGN=MIDDLE  ALT=\"a=x\"   DISABLED_style= \"max-width:90%; height:auto;\" > (this is the width), <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=x%2B4 ALIGN=MIDDLE  ALT=\"b=x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > (this is the height), and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=sqrt%28194%29%2F2 ALIGN=MIDDLE  ALT=\"c=sqrt%28194%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > (which is given as the diagonal)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B%28x%2B4%29%5E2=194%2F4 ALIGN=MIDDLE  ALT=\"x%5E2%2B%28x%2B4%29%5E2=194%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28194%29%2F2 ALIGN=MIDDLE  ALT=\"sqrt%28194%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=194%2F4 ALIGN=MIDDLE  ALT=\"194%2F4\"   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%5E2%2B%28x%2B4%29%5E2=97%2F2 ALIGN=MIDDLE  ALT=\"x%5E2%2B%28x%2B4%29%5E2=97%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2Bx%5E2%2B8x%2B16=97%2F2 ALIGN=MIDDLE  ALT=\"x%5E2%2Bx%5E2%2B8x%2B16=97%2F2\"   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=2x%5E2%2B8x%2B16=97%2F2 ALIGN=MIDDLE  ALT=\"2x%5E2%2B8x%2B16=97%2F2\"   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=4x%5E2%2B16x%2B32=97 ALIGN=MIDDLE  ALT=\"4x%5E2%2B16x%2B32=97\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <b>every</b> term by the LCD 2 to clear the fraction\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2%2B16x-65=0 ALIGN=MIDDLE  ALT=\"4x%5E2%2B16x-65=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 97 from both sides.\r<BR>\n" );
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document.write( "Notice we have a quadratic equation in the form of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=4 ALIGN=MIDDLE  ALT=\"a=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=16 ALIGN=MIDDLE  ALT=\"b=16\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-65 ALIGN=MIDDLE  ALT=\"c=-65\"   DISABLED_style= \"max-width:90%; height:auto;\" >\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-%2816%29+%2B-+sqrt%28+%2816%29%5E2-4%284%29%28-65%29+%29%29%2F%282%284%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-%2816%29+%2B-+sqrt%28+%2816%29%5E2-4%284%29%28-65%29+%29%29%2F%282%284%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=4 ALIGN=MIDDLE  ALT=\"a=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=16 ALIGN=MIDDLE  ALT=\"b=16\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-65 ALIGN=MIDDLE  ALT=\"c=-65\"   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+=+%28-16+%2B-+sqrt%28+256-4%284%29%28-65%29+%29%29%2F%282%284%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-16+%2B-+sqrt%28+256-4%284%29%28-65%29+%29%29%2F%282%284%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16 ALIGN=MIDDLE  ALT=\"16\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=256 ALIGN=MIDDLE  ALT=\"256\"   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+=+%28-16+%2B-+sqrt%28+256--1040+%29%29%2F%282%284%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-16+%2B-+sqrt%28+256--1040+%29%29%2F%282%284%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%284%29%28-65%29 ALIGN=MIDDLE  ALT=\"4%284%29%28-65%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1040 ALIGN=MIDDLE  ALT=\"-1040\"   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+=+%28-16+%2B-+sqrt%28+256%2B1040+%29%29%2F%282%284%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-16+%2B-+sqrt%28+256%2B1040+%29%29%2F%282%284%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28256--1040%29 ALIGN=MIDDLE  ALT=\"sqrt%28256--1040%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28256%2B1040%29 ALIGN=MIDDLE  ALT=\"sqrt%28256%2B1040%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+=+%28-16+%2B-+sqrt%28+1296+%29%29%2F%282%284%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-16+%2B-+sqrt%28+1296+%29%29%2F%282%284%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=256 ALIGN=MIDDLE  ALT=\"256\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1040 ALIGN=MIDDLE  ALT=\"1040\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1296 ALIGN=MIDDLE  ALT=\"1296\"   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+=+%28-16+%2B-+sqrt%28+1296+%29%29%2F%288%29 ALIGN=MIDDLE  ALT=\"x+=+%28-16+%2B-+sqrt%28+1296+%29%29%2F%288%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=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8 ALIGN=MIDDLE  ALT=\"8\"   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+=+%28-16+%2B-+36%29%2F%288%29 ALIGN=MIDDLE  ALT=\"x+=+%28-16+%2B-+36%29%2F%288%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=1296 ALIGN=MIDDLE  ALT=\"1296\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36 ALIGN=MIDDLE  ALT=\"36\"   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+=+%28-16+%2B+36%29%2F%288%29 ALIGN=MIDDLE  ALT=\"x+=+%28-16+%2B+36%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+=+%28-16+-+36%29%2F%288%29 ALIGN=MIDDLE  ALT=\"x+=+%28-16+-+36%29%2F%288%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+=+%2820%29%2F%288%29 ALIGN=MIDDLE  ALT=\"x+=+%2820%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+=++%28-52%29%2F%288%29 ALIGN=MIDDLE  ALT=\"x+=++%28-52%29%2F%288%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+=+5%2F2 ALIGN=MIDDLE  ALT=\"x+=+5%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-13%2F2 ALIGN=MIDDLE  ALT=\"x+=+-13%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify. \r<BR>\n" );
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document.write( "So the possible widths are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+5%2F2 ALIGN=MIDDLE  ALT=\"x+=+5%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-13%2F2 ALIGN=MIDDLE  ALT=\"x+=+-13%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > (which in decimal form are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2.5 ALIGN=MIDDLE  ALT=\"x=2.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-6.5 ALIGN=MIDDLE  ALT=\"x=-6.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > respectively)\r<BR>\n" );
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document.write( "However, since a negative width doesn't make sense, this means that the only solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+5%2F2 ALIGN=MIDDLE  ALT=\"x+=+5%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > (which is the mixed fraction <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2%261%2F2 ALIGN=MIDDLE  ALT=\"x=2%261%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "So the width is 2 and a half feet\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B4 ALIGN=MIDDLE  ALT=\"x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Go back to the expression that represents the height\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%261%2F2%2B4 ALIGN=MIDDLE  ALT=\"2%261%2F2%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2%261%2F2 ALIGN=MIDDLE  ALT=\"x=2%261%2F2\"   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=6%261%2F2 ALIGN=MIDDLE  ALT=\"6%261%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add\r<BR>\n" );
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document.write( "So the height of the door is 6 and a half feet.\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So the dimensions of the door are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%261%2F2 ALIGN=MIDDLE  ALT=\"2%261%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > feet by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%261%2F2 ALIGN=MIDDLE  ALT=\"6%261%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > which means that the answer is B) 2 1/2 ft by 6 1/2 ft </SPAN>\n" );
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