document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=119171>Question 119171</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0395535921/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> i have another ?\r<BR>\n" );
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document.write( "The longer leg of a right triangle has length 1cm less than twice the shorter leg. the hypotenuse has length 1cm greater than the shorter leg. find the lengths of the three sides of the triangle.\r<BR>\n" );
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document.write( "i have:<BR>\n" );
document.write( "x<BR>\n" );
document.write( "1-x<BR>\n" );
document.write( "2x-1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #87278 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=87278\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I presume x to be the short leg, so your 2x - 1 representation would be correct for the longer leg, but the hypotenuse is then x + 1 rather than 1 - x.\r<BR>\n" );
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document.write( "Using Pythagoras:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B1%29%5E2=x%5E2%2B%282x-1%29%5E2 ALIGN=MIDDLE  ALT=\"%28x%2B1%29%5E2=x%5E2%2B%282x-1%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Expand the binomials, collect terms, and solve<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B2x%2B1=x%5E2%2B4x%5E2-4x%2B1 ALIGN=MIDDLE  ALT=\"x%5E2%2B2x%2B1=x%5E2%2B4x%5E2-4x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2-6x=0 ALIGN=MIDDLE  ALT=\"4x%5E2-6x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%284x-6%29=0 ALIGN=MIDDLE  ALT=\"x%284x-6%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3%2F2 ALIGN=MIDDLE  ALT=\"x=3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  But we can exclude the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > root because that would mean that all three sides of the triangle were of length 0 -- a very uninteresting triangle indeed.  So, the short leg is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F2 ALIGN=MIDDLE  ALT=\"3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >cm, the hypotenuse is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F2%2B1=5%2F2 ALIGN=MIDDLE  ALT=\"3%2F2%2B1=5%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >cm and the long leg is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%283%2F2%29-1=3-1=2 ALIGN=MIDDLE  ALT=\"2%283%2F2%29-1=3-1=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >cm.\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=sqrt%28%283%2F2%29%5E2%2B%284%2F2%29%5E2%29%29 ALIGN=MIDDLE  ALT=\"sqrt%28%283%2F2%29%5E2%2B%284%2F2%29%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > =<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%289%2F4%29%2B%2816%2F4%29%29 ALIGN=MIDDLE  ALT=\"sqrt%28%289%2F4%29%2B%2816%2F4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > =<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2825%29%2Fsqrt%284%29=5%2F2 ALIGN=MIDDLE  ALT=\"sqrt%2825%29%2Fsqrt%284%29=5%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, Check!\r<BR>\n" );
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document.write( "Hope that helps.<BR>\n" );
document.write( "John </SPAN>\n" );
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