document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=183395>Question 183395</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A rectangular parcel of land is 70 feet longer than it is wide. Each diagonal is 130 feet long. What are the dimensions of the parcel?\r<BR>\n" );
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document.write( "I know you have to use the pythagorean theorem but I have no clue what to do. Please help! :) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #137687 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=137687\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let L=length and W=width\r<BR>\n" );
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document.write( "Since the \"land is 70 feet longer than it is wide\", this tells us that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=W%2B70 ALIGN=MIDDLE  ALT=\"L=W%2B70\"   DISABLED_style= \"max-width:90%; height:auto;\" > (ie take the width and add 70 to get the length)\r<BR>\n" );
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document.write( "If you cut the rectangle in half along the diagonal, you'll find that the resulting pieces will be right triangles. So we can use Pythagorean's Theorem to find the legs (since we're given the hypotenuse)\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 Pythagorean's Theorem\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%5E2%2BW%5E2=130%5E2 ALIGN=MIDDLE  ALT=\"L%5E2%2BW%5E2=130%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=L ALIGN=MIDDLE  ALT=\"a=L\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=W ALIGN=MIDDLE  ALT=\"b=W\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=130 ALIGN=MIDDLE  ALT=\"c=130\"   DISABLED_style= \"max-width:90%; height:auto;\" > (this is the given diagonal)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%5E2%2BW%5E2=16900 ALIGN=MIDDLE  ALT=\"L%5E2%2BW%5E2=16900\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square 130 to get 16900\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28W%2B70%29%5E2%2BW%5E2=16900 ALIGN=MIDDLE  ALT=\"%28W%2B70%29%5E2%2BW%5E2=16900\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=W%2B70 ALIGN=MIDDLE  ALT=\"L=W%2B70\"   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%5E2%2B140W%2B4900%2BW%5E2=16900 ALIGN=MIDDLE  ALT=\"W%5E2%2B140W%2B4900%2BW%5E2=16900\"   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=W%5E2%2B140W%2B4900%2BW%5E2-16900=0 ALIGN=MIDDLE  ALT=\"W%5E2%2B140W%2B4900%2BW%5E2-16900=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 16900 from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2W%5E2%2B140W-12000=0 ALIGN=MIDDLE  ALT=\"2W%5E2%2B140W-12000=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "Notice how the equation is now in the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=2 ALIGN=MIDDLE  ALT=\"a=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=140 ALIGN=MIDDLE  ALT=\"b=140\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-12000 ALIGN=MIDDLE  ALT=\"c=-12000\"   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+=+%28-140+%2B-+sqrt%28+%28140%29%5E2-4%2A2%2A-12000+%29%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"W+=+%28-140+%2B-+sqrt%28+%28140%29%5E2-4%2A2%2A-12000+%29%29%2F%282%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=2 ALIGN=MIDDLE  ALT=\"a=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=140 ALIGN=MIDDLE  ALT=\"b=140\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-12000 ALIGN=MIDDLE  ALT=\"c=-12000\"   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+=+%28-140+%2B-+sqrt%28+19600-4%2A2%2A-12000+%29%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"W+=+%28-140+%2B-+sqrt%28+19600-4%2A2%2A-12000+%29%29%2F%282%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square 140 to get 19600\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W+=+%28-140+%2B-+sqrt%28+19600%2B96000+%29%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"W+=+%28-140+%2B-+sqrt%28+19600%2B96000+%29%29%2F%282%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2A-12000%2A2 ALIGN=MIDDLE  ALT=\"-4%2A-12000%2A2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get 96000\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W+=+%28-140+%2B-+sqrt%28+115600+%29%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"W+=+%28-140+%2B-+sqrt%28+115600+%29%29%2F%282%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms in the radicand (everything under the square root)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W+=+%28-140+%2B-+340%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"W+=+%28-140+%2B-+340%29%2F%282%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify the square root \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W+=+%28-140+%2B-+340%29%2F4 ALIGN=MIDDLE  ALT=\"W+=+%28-140+%2B-+340%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and 2 to get 4\r<BR>\n" );
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document.write( "So now the expression breaks down into two parts\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W+=+%28-140+%2B+340%29%2F4 ALIGN=MIDDLE  ALT=\"W+=+%28-140+%2B+340%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-140+-+340%29%2F4 ALIGN=MIDDLE  ALT=\"x+=+%28-140+-+340%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Lets look at the first part:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W=%28-140+%2B+340%29%2F4 ALIGN=MIDDLE  ALT=\"W=%28-140+%2B+340%29%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=W=200%2F4 ALIGN=MIDDLE  ALT=\"W=200%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add the terms in the numerator\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W=50 ALIGN=MIDDLE  ALT=\"W=50\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide\r<BR>\n" );
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document.write( "So one possible answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W=50 ALIGN=MIDDLE  ALT=\"W=50\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now lets look at the second part:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W=%28-140+-+340%29%2F4 ALIGN=MIDDLE  ALT=\"W=%28-140+-+340%29%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=W=-480%2F4 ALIGN=MIDDLE  ALT=\"W=-480%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract the terms in the numerator\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W=-120 ALIGN=MIDDLE  ALT=\"W=-120\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide\r<BR>\n" );
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document.write( "So another possible answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W=-120 ALIGN=MIDDLE  ALT=\"W=-120\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "However, it doesn't make sense to have a negative width. So we must ignore this possible solution\r<BR>\n" );
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document.write( "So this means that the only answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W=50 ALIGN=MIDDLE  ALT=\"W=50\"   DISABLED_style= \"max-width:90%; height:auto;\" > and that the width is 50 feet.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=W%2B70 ALIGN=MIDDLE  ALT=\"L=W%2B70\"   DISABLED_style= \"max-width:90%; height:auto;\" > Go back to the first equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=50%2B70 ALIGN=MIDDLE  ALT=\"L=50%2B70\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W=50 ALIGN=MIDDLE  ALT=\"W=50\"   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=L=120 ALIGN=MIDDLE  ALT=\"L=120\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add\r<BR>\n" );
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document.write( "So the other answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=120 ALIGN=MIDDLE  ALT=\"L=120\"   DISABLED_style= \"max-width:90%; height:auto;\" > which means that the length is 120 feet.\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So the length is 120 feet and the width is 50 feet. </SPAN>\n" );
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