document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=132345>Question 132345</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need some help on this problem please:  find out the length of sides a & b on the following triangle. A=x, b=3x and c = 19.  I think I should use the pythagorean theorem.  I squared 19 to get 361, but I don't know how to figure the rest. Any advice would be great. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #96703 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=96703\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You don't say, and I certainly can't see the figure, but I'll just assume that you have a right triangle and that side c is the hypotenuse.  Given those assumptions, the Pythagorean Theorem is the correct approach to the solution.\r<BR>\n" );
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document.write( "We know that <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;\" >, so let's substitute the given values and see where it takes us.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B%283x%29%5E2=19%5E2 ALIGN=MIDDLE  ALT=\"x%5E2%2B%283x%29%5E2=19%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=x%5E2%2B9x%5E2=19%5E2 ALIGN=MIDDLE  ALT=\"x%5E2%2B9x%5E2=19%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=10x%5E2=19%5E2 ALIGN=MIDDLE  ALT=\"10x%5E2=19%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=x%5E2=19%5E2%2F10 ALIGN=MIDDLE  ALT=\"x%5E2=19%5E2%2F10\"   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=sqrt%2819%5E2%2F10%29=sqrt%2819%5E2%29%2Fsqrt%2810%29=19%2Fsqrt%2810%29 ALIGN=MIDDLE  ALT=\"x=sqrt%2819%5E2%2F10%29=sqrt%2819%5E2%29%2Fsqrt%2810%29=19%2Fsqrt%2810%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=19%2Fsqrt%2810%29 ALIGN=MIDDLE  ALT=\"19%2Fsqrt%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is certainly an answer to the problem, but it is not in simplest terms because of the radical in the denominator.  Simplest terms demands that, if possible, the denominator must be a rational number.\r<BR>\n" );
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document.write( "So, we need to perform a process called rationalizing the denominator.  In this case, all we need to do is multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=19%2Fsqrt%2810%29 ALIGN=MIDDLE  ALT=\"19%2Fsqrt%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > in the form of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2810%29%2Fsqrt%2810%29 ALIGN=MIDDLE  ALT=\"sqrt%2810%29%2Fsqrt%2810%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=%2819%2Fsqrt%2810%29%29%28sqrt%2810%29%2Fsqrt%2810%29%29=19sqrt%2810%29%2F10 ALIGN=MIDDLE  ALT=\"%2819%2Fsqrt%2810%29%29%28sqrt%2810%29%2Fsqrt%2810%29%29=19sqrt%2810%29%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Final answer, Regis. </SPAN>\n" );
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