document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=93459>Question 93459</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1. The length of one leg of a right triangle is 6 cm more than the other. If the length of the hypotenuse is 18 cm, what are the lengths of the two legs? Please give the answer in ascending order rounded to the nearest tenth of a cm.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #68041 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=68041\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "Let x=leg #1, y=leg #2\r<BR>\n" );
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document.write( "Since the length of one leg of a right triangle is 6 cm more than the other, this means we can write\r<BR>\n" );
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document.write( "Now lets use Pythagorean's theorem to set up the problem\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%2B6%29%5E2=18%5E2 ALIGN=MIDDLE  ALT=\"x%5E2%2B%28x%2B6%29%5E2=18%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in the hypotenuse h=18 and y=x+6\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%2B12x%2B36=18%5E2 ALIGN=MIDDLE  ALT=\"x%5E2%2Bx%5E2%2B12x%2B36=18%5E2\"   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%2B12x%2B36=324 ALIGN=MIDDLE  ALT=\"2x%5E2%2B12x%2B36=324\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square 18\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%2B12x%2B36-324=0 ALIGN=MIDDLE  ALT=\"2x%5E2%2B12x%2B36-324=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 324 from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%2B12x-288=0 ALIGN=MIDDLE  ALT=\"2x%5E2%2B12x-288=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\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( "Starting with the general quadratic\r<BR>\n" );
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document.write( "<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;\" >\r<BR>\n" );
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document.write( "the general solution using the quadratic equation is:\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%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29 ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So lets solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Ax%5E2%2B12%2Ax-288=0 ALIGN=MIDDLE  ALT=\"2%2Ax%5E2%2B12%2Ax-288=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( notice <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=12 ALIGN=MIDDLE  ALT=\"b=12\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-288 ALIGN=MIDDLE  ALT=\"c=-288\"   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+=+%28-12+%2B-+sqrt%28+%2812%29%5E2-4%2A2%2A-288+%29%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"x+=+%28-12+%2B-+sqrt%28+%2812%29%5E2-4%2A2%2A-288+%29%29%2F%282%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=2, b=12, and c=-288\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-12+%2B-+sqrt%28+144-4%2A2%2A-288+%29%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"x+=+%28-12+%2B-+sqrt%28+144-4%2A2%2A-288+%29%29%2F%282%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square 12 to get 144  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-12+%2B-+sqrt%28+144%2B2304+%29%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"x+=+%28-12+%2B-+sqrt%28+144%2B2304+%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-288%2A2 ALIGN=MIDDLE  ALT=\"-4%2A-288%2A2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2304 ALIGN=MIDDLE  ALT=\"2304\"   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+=+%28-12+%2B-+sqrt%28+2448+%29%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"x+=+%28-12+%2B-+sqrt%28+2448+%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=x+=+%28-12+%2B-+12%2Asqrt%2817%29%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"x+=+%28-12+%2B-+12%2Asqrt%2817%29%29%2F%282%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify the square root (note: If you need help with simplifying the square root, check out this <a  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Radicals/simplifying-square-roots.solver> solver</a>)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-12+%2B-+12%2Asqrt%2817%29%29%2F4 ALIGN=MIDDLE  ALT=\"x+=+%28-12+%2B-+12%2Asqrt%2817%29%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=x+=+%28-12+%2B+12%2Asqrt%2817%29%29%2F4 ALIGN=MIDDLE  ALT=\"x+=+%28-12+%2B+12%2Asqrt%2817%29%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-12+-+12%2Asqrt%2817%29%29%2F4 ALIGN=MIDDLE  ALT=\"x+=+%28-12+-+12%2Asqrt%2817%29%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now break up the fraction\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-12%2F4%2B12%2Asqrt%2817%29%2F4 ALIGN=MIDDLE  ALT=\"x=-12%2F4%2B12%2Asqrt%2817%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-12%2F4-12%2Asqrt%2817%29%2F4 ALIGN=MIDDLE  ALT=\"x=-12%2F4-12%2Asqrt%2817%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3+%2B3%2Asqrt%2817%29 ALIGN=MIDDLE  ALT=\"x=-3+%2B3%2Asqrt%2817%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3-3%2Asqrt%2817%29 ALIGN=MIDDLE  ALT=\"x=-3-3%2Asqrt%2817%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So these expressions approximate to\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=9.36931687685298 ALIGN=MIDDLE  ALT=\"x=9.36931687685298\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-15.369316876853 ALIGN=MIDDLE  ALT=\"x=-15.369316876853\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So our possible solutions are:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=9.36931687685298 ALIGN=MIDDLE  ALT=\"x=9.36931687685298\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-15.369316876853 ALIGN=MIDDLE  ALT=\"x=-15.369316876853\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since a negative length doesn't make sense, our only solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=9.36931687685298 ALIGN=MIDDLE  ALT=\"x=9.36931687685298\"   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( "First find y\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=9.369%2B6=15.369 ALIGN=MIDDLE  ALT=\"y=9.369%2B6=15.369\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now plug in the triangle's dimensions\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9.369%5E2%2B15.369%5E2=18%5E2 ALIGN=MIDDLE  ALT=\"9.369%5E2%2B15.369%5E2=18%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=323.984322=324 ALIGN=MIDDLE  ALT=\"323.984322=324\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify. Since we rounded, this is as close as it gets. So our answer is verified. </SPAN>\n" );
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