document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=805425>Question 805425</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this equation: In the annual Pythagoras Triathlon, competitors swim, bike, and run. Each portion of the race is the side of a right triangle. The run portion is 1.12 miles, and the bike portion is 1.13 miles. When Russ heard someone say the swim portion represented the hypotenuse of the race course, he almost fainted. But then he learned that the hypotenuse was the bike portion, and he breathed a sigh of relief. \r<BR>\n" );
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document.write( "How much shorter is the swim portion than he originally thought?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #485231 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=485231\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Russ thought that the right triangle was like this (with the distances in miles): <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-0.5%2C1.5%2C-0.5%2C1.5%2C%0D%0Atriangle%280%2C0%2C1.13%2C0%2C0%2C1.12%29%2C%0D%0Arectangle%280%2C0%2C0.05%2C0.05%29%2C%0D%0Alocate%280.26%2C0%2Cbike%29%2Clocate%280.49%2C0%2Cportion%29%2Clocate%280.35%2C0.1%2C1.13%29%2C%0D%0Alocate%280.01%2C0.6%2Crun%29%2Clocate%280.01%2C0.5%2Cportion%29%2Clocate%28-0.22%2C0.55%2C1.12%29%2C%0D%0Alocate%280.54%2C0.7%2Ca=swim%29%2Clocate%280.62%2C0.6%2Cportion%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "That would make the swim portion longest, because the Pythagorean theorem says that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2=1.12%5E2%2B1.13%5E2 ALIGN=MIDDLE  ALT=\"a%5E2=1.12%5E2%2B1.13%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2=1.2544%2B1.2769 ALIGN=MIDDLE  ALT=\"a%5E2=1.2544%2B1.2769\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2=2.5313 ALIGN=MIDDLE  ALT=\"a%5E2=2.5313\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=sqrt%282.5313%29 ALIGN=MIDDLE  ALT=\"a=sqrt%282.5313%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28a=1.59%29 ALIGN=MIDDLE  ALT=\"highlight%28a=1.59%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (rounded)<BR>\n" );
document.write( "It turns out that the race is like this (drawing not to scale for good reason): <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28150%2C300%2C-0.3%2C0.7%2C-0.5%2C1.5%2C%0D%0Atriangle%280%2C0%2C0.5%2C0%2C0%2C1.13%29%2Crectangle%280%2C0%2C0.05%2C0.05%29%2C%0D%0Alocate%280.01%2C0.5%2Crun%29%2Clocate%280.01%2C0.4%2Cportion%29%2Clocate%28-0.22%2C0.45%2C1.12%29%2C%0D%0Alocate%28-0.1%2C0%2Cb=swim%29%2Clocate%280.3%2C0%2Cportion%29%2Clocate%280.2%2C0.8%2C1.13%29%2C%0D%0Alocate%280.25%2C0.7%2Cbike%29%2Clocate%280.3%2C0.6%2Cportion%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "In this case, the Pythagorean theorem says that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2%2B1.12%5E3=1.13%5E2 ALIGN=MIDDLE  ALT=\"b%5E2%2B1.12%5E3=1.13%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2=1.2769-1.2544 ALIGN=MIDDLE  ALT=\"b%5E2=1.2769-1.2544\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2=0.0225 ALIGN=MIDDLE  ALT=\"b%5E2=0.0225\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=sqrt%280.0225%29 ALIGN=MIDDLE  ALT=\"b=sqrt%280.0225%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28b=0.15%29 ALIGN=MIDDLE  ALT=\"highlight%28b=0.15%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (exactly)<BR>\n" );
document.write( "The difference (rounded) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%281.44miles%29 ALIGN=MIDDLE  ALT=\"highlight%281.44miles%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a-b=1.59-0.15=highlight%281.44%29 ALIGN=MIDDLE  ALT=\"a-b=1.59-0.15=highlight%281.44%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "NOTE:<BR>\n" );
document.write( "If I had made the last triangle to scale it would have been such a narrow, tall triangle that it would have been useless to illustrate the problem (so I made it wider). </SPAN>\n" );
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