document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=765200>Question 765200</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The area of a rectangle is 5000 ft^2. The diagonal is 10 feet longer than the length. What are the dimensions of the rectangle rounded to the nearest foot. <BR>\n" );
document.write( "The prompt says that this can be done on the calculator, but I can't wrap my head around it.<BR>\n" );
document.write( "Any help would be appreciated! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #466008 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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/cgi-bin/show-face.mpl?user=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=466008\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The area of a rectangle is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=L%2AW=5000ft%5E2 ALIGN=MIDDLE  ALT=\"A=L%2AW=5000ft%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "The diagonal <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d ALIGN=MIDDLE  ALT=\"d\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10ft ALIGN=MIDDLE  ALT=\"10ft\"   DISABLED_style= \"max-width:90%; height:auto;\" > longer than the length <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L ALIGN=MIDDLE  ALT=\"L\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The diagonal <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d ALIGN=MIDDLE  ALT=\"d\"   DISABLED_style= \"max-width:90%; height:auto;\" > divides rectangle into two right angle triangles, and we can use Pythagorean theorem:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5E2=L%5E2%2BW%5E2 ALIGN=MIDDLE  ALT=\"d%5E2=L%5E2%2BW%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d ALIGN=MIDDLE  ALT=\"d\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10ft ALIGN=MIDDLE  ALT=\"10ft\"   DISABLED_style= \"max-width:90%; height:auto;\" > longer than the length <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L ALIGN=MIDDLE  ALT=\"L\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=L%2B10ft ALIGN=MIDDLE  ALT=\"d=L%2B10ft\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, substitute it in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5E2=L%5E2%2BW%5E2 ALIGN=MIDDLE  ALT=\"d%5E2=L%5E2%2BW%5E2\"   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=d=sqrt%28L%5E2%2BW%5E2%29 ALIGN=MIDDLE  ALT=\"d=sqrt%28L%5E2%2BW%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and we are told that this is 10 feet longer than one side,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28L%5E2%2BW%5E2%29=L%2B10ft ALIGN=MIDDLE  ALT=\"sqrt%28L%5E2%2BW%5E2%29=L%2B10ft\"   DISABLED_style= \"max-width:90%; height:auto;\" >........square both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%28L%5E2%2BW%5E2%29%29%5E2=%28L%2B10ft%29%5E2 ALIGN=MIDDLE  ALT=\"%28sqrt%28L%5E2%2BW%5E2%29%29%5E2=%28L%2B10ft%29%5E2\"   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%5E2%2BW%5E2=L%5E2%2B20Lft%2B10oft%5E2 ALIGN=MIDDLE  ALT=\"L%5E2%2BW%5E2=L%5E2%2B20Lft%2B10oft%5E2\"   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=20Lft%2B100ft%5E2 ALIGN=MIDDLE  ALT=\"W%5E2=20Lft%2B100ft%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "go to  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=L%2AW=5000ft%5E2 ALIGN=MIDDLE  ALT=\"A=L%2AW=5000ft%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and solve it for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L ALIGN=MIDDLE  ALT=\"L\"   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=5000%2FW ALIGN=MIDDLE  ALT=\"L=5000%2FW\"   DISABLED_style= \"max-width:90%; height:auto;\" >......plug it in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W%5E2=20L%2B100 ALIGN=MIDDLE  ALT=\"W%5E2=20L%2B100\"   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=20%285000%2FW%29%2B100 ALIGN=MIDDLE  ALT=\"W%5E2=20%285000%2FW%29%2B100\"   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=%28100000%2FW%29%2B100 ALIGN=MIDDLE  ALT=\"W%5E2=%28100000%2FW%29%2B100\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....multiply by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W ALIGN=MIDDLE  ALT=\"W\"   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%2AW=W%28100000%2FW%29%2B100W ALIGN=MIDDLE  ALT=\"W%5E2%2AW=W%28100000%2FW%29%2B100W\"   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%2AW=cross%28W%29%28100000%2Fcross%28W%29%29%2B100W ALIGN=MIDDLE  ALT=\"W%5E2%2AW=cross%28W%29%28100000%2Fcross%28W%29%29%2B100W\"   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%5E3=100000%2B100W ALIGN=MIDDLE  ALT=\"W%5E3=100000%2B100W\"   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%5E3-100W-100000=0 ALIGN=MIDDLE  ALT=\"W%5E3-100W-100000=0\"   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=47.134ft ALIGN=MIDDLE  ALT=\"W=47.134ft\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "now find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L ALIGN=MIDDLE  ALT=\"L\"   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=5000ft%5E2%2FW ALIGN=MIDDLE  ALT=\"L=5000ft%5E2%2FW\"   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=5000ft%5E2%2F47.134ft ALIGN=MIDDLE  ALT=\"L=5000ft%5E2%2F47.134ft\"   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=106.08ft ALIGN=MIDDLE  ALT=\"L=106.08ft\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "check:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=L%2AW=5000ft%5E2 ALIGN=MIDDLE  ALT=\"A=L%2AW=5000ft%5E2\"   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=A=106.08ft%2A47.134ft=5000ft%5E2 ALIGN=MIDDLE  ALT=\"A=106.08ft%2A47.134ft=5000ft%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=106.08ft ALIGN=MIDDLE  ALT=\"L=106.08ft\"   DISABLED_style= \"max-width:90%; height:auto;\" > then diagonal is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=106.08ft%2B10ft=116.08ft ALIGN=MIDDLE  ALT=\"d=106.08ft%2B10ft=116.08ft\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "check if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5E2=L%5E2%2BW%5E2 ALIGN=MIDDLE  ALT=\"d%5E2=L%5E2%2BW%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28116.08ft%29%5E2=%28106.08ft%29%5E2%2B%2847.134ft%29%5E2 ALIGN=MIDDLE  ALT=\"%28116.08ft%29%5E2=%28106.08ft%29%5E2%2B%2847.134ft%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13474.5664ft%5E2=11252.9664ft%5E2%2B2221.613956ft%5E2 ALIGN=MIDDLE  ALT=\"13474.5664ft%5E2=11252.9664ft%5E2%2B2221.613956ft%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13474.5664ft%5E2=13474.58+ft%5E2+ ALIGN=MIDDLE  ALT=\"13474.5664ft%5E2=13474.58+ft%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > rounded to whole number\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13475ft%5E2=13475+ft%5E2+ ALIGN=MIDDLE  ALT=\"13475ft%5E2=13475+ft%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
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