document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=113059>Question 113059</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how do you figure triangles with a square root in the problem. I have a 90degree triangle with the hypotenus being 6 square root 3 and I have to find the legs. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #82346 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=82346\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You really can't solve this problem the way you posed it because there are an infinite number of different right triangles with a hypotenuse = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"6%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Now if you had specified this was an isoceles right triangle, meaning both of the legs were of equal length or if you had specified any other proportional relationship between the length of the legs, then the problem becomes solveable.\r<BR>\n" );
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document.write( "I'm going to assume you meant an isoceles right triangle and solve this.\r<BR>\n" );
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document.write( "Pythagoras tells us that for any right triangle of sides a, b, and hypotenuse c, the following relationship is true:\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;\" >\r<BR>\n" );
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document.write( "We are given that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=6%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"c=6%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2=36%2A3=108 ALIGN=MIDDLE  ALT=\"c%5E2=36%2A3=108\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "So now we can write:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2Bb%5E2=108 ALIGN=MIDDLE  ALT=\"a%5E2%2Bb%5E2=108\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "But, since we are assuming that this is an isoceles right triangle, a = b, so we can now write:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2Ba%5E2=108 ALIGN=MIDDLE  ALT=\"a%5E2%2Ba%5E2=108\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So now, let's simplify and solve:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a%5E2=108 ALIGN=MIDDLE  ALT=\"2a%5E2=108\"   DISABLED_style= \"max-width:90%; height:auto;\" >, combine like terms<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2=54 ALIGN=MIDDLE  ALT=\"a%5E2=54\"   DISABLED_style= \"max-width:90%; height:auto;\" >, divide both sides by 2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=sqrt%2854%29=sqrt%286%2A9%29=3%2Asqrt%286%29 ALIGN=MIDDLE  ALT=\"a=sqrt%2854%29=sqrt%286%2A9%29=3%2Asqrt%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, take the square root of both sides. Done.\r<BR>\n" );
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document.write( "Except we should check our answer:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2Asqrt%286%29%29%5E2%2B%283%2Asqrt%286%29%29%5E2=%286%2Asqrt%283%29%29%5E2 ALIGN=MIDDLE  ALT=\"%283%2Asqrt%286%29%29%5E2%2B%283%2Asqrt%286%29%29%5E2=%286%2Asqrt%283%29%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289%2A6%29%2B%289%2A6%29=108 ALIGN=MIDDLE  ALT=\"%289%2A6%29%2B%289%2A6%29=108\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=54%2B54=108 ALIGN=MIDDLE  ALT=\"54%2B54=108\"   DISABLED_style= \"max-width:90%; height:auto;\" >, Checks.\r<BR>\n" );
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document.write( "Now what if one leg of the triangle had been specified to be three times longer than the other?\r<BR>\n" );
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document.write( "Then, instead of a =  b, we would say that 3a = b,<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2B9a%5E2=108 ALIGN=MIDDLE  ALT=\"a%5E2%2B9a%5E2=108\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10a%5E2=108 ALIGN=MIDDLE  ALT=\"10a%5E2=108\"   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=10.8 ALIGN=MIDDLE  ALT=\"a%5E2=10.8\"   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%2810.8%29 ALIGN=MIDDLE  ALT=\"a=sqrt%2810.8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=3%2Asqrt%2810.8%29 ALIGN=MIDDLE  ALT=\"b=3%2Asqrt%2810.8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Hope this helps,<BR>\n" );
document.write( "John\r<BR>\n" );
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document.write( " </SPAN>\n" );
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