document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=149780>Question 149780</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The hypotenuse of a right triangle is 7 less than three times the shortest leg.  The longest leg is two less than the hypotenuse.  Detemine the lengths of all three sides.  There are two sets of answers, state both of them. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #109899 by </B><A HREF=/tutors/aboutme.mpl?userid=kmcruz09><B>kmcruz09(38)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=kmcruz09><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=109899\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The hypotenuse of a right triangle is 7 less than three times the shortest leg.  The longest leg is two less than the hypotenuse.  Detemine the lengths of all three sides.  There are two sets of answers, state both of them.\r<BR>\n" );
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document.write( "let x = shortest leg<BR>\n" );
document.write( "then 3x-7 = hypotenuse<BR>\n" );
document.write( "then 3x-9 = longest leg\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-9%29%5E2+=+%283x-7%29%5E2 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+%283x-9%29%5E2+=+%283x-7%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=x%5E2+%2B+9x%5E2+-54x+%2B81+=+9x%5E2-42x%2B49 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+9x%5E2+-54x+%2B81+=+9x%5E2-42x%2B49\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+54x+%2B+81+=+-42x+%2B+49 ALIGN=MIDDLE  ALT=\"x%5E2+-+54x+%2B+81+=+-42x+%2B+49\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+12x+%2B+32+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+-+12x+%2B+32+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-8%29%28x-4%29=0 ALIGN=MIDDLE  ALT=\"%28x-8%29%28x-4%29=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=8 ALIGN=MIDDLE  ALT=\"x=8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4 ALIGN=MIDDLE  ALT=\"x=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Triangle 1 : 8, 17, 15<BR>\n" );
document.write( "Triangle 2: 4, 5, 3\r<BR>\n" );
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document.write( "in the case of Triangle 2, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x-9 ALIGN=MIDDLE  ALT=\"3x-9\"   DISABLED_style= \"max-width:90%; height:auto;\" > is equal to 3. It doesn't satisfy the conditions given in the problem that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x-9 ALIGN=MIDDLE  ALT=\"3x-9\"   DISABLED_style= \"max-width:90%; height:auto;\" > must be the longest leg. Therefore, the sides of Triangle 1 should be considered as the only correct answer. </SPAN>\n" );
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