document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=689216>Question 689216</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help in setting up an equation.  The problem says the longer leg of a right triangle is 3 cm less than 5 times the shorter leg.  The hypotenuse is 3 cm longer than the shorter leg.  Find the length of the shorter leg.  a^2 + b^2 = c^2 or in this case b^2 + (5b - 3)^2 = (5b + 3)^2.  I am having problems once I get the equation to 26b^2 - 30B +9 = 25b^2 + 30B +9.  Can someone help me from that point or tell me where I went wrong in setting the problem up?   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #425879 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=425879\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If \"the longer leg of a right triangle is 3 cm less than 5 times the shorter leg,\"   <BR>\n" );
document.write( "you are correct in translating<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+%2B+b%5E2+=+c%5E2 ALIGN=MIDDLE  ALT=\"a%5E2+%2B+b%5E2+=+c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2+%2B+%285b+-+3%29%5E2+=+c%5E2 ALIGN=MIDDLE  ALT=\"b%5E2+%2B+%285b+-+3%29%5E2+=+c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, calling the shorter leg <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( " <BR>\n" );
document.write( "However, if the problem says exactly that the \"hypotenuse is 3 cm longer than the shorter leg,\" it should be<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b%5E2+%2B+%285b+-+3%29%5E2+=+%28b+%2B+3%29%5E2 ALIGN=MIDDLE  ALT=\"+b%5E2+%2B+%285b+-+3%29%5E2+=+%28b+%2B+3%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > instead of <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2+%2B+%285b+-+3%29%5E2+=+%285b+%2B+3%29%5E2 ALIGN=MIDDLE  ALT=\"b%5E2+%2B+%285b+-+3%29%5E2+=+%285b+%2B+3%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Then,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b%5E2+%2B+%285b+-+3%29%5E2+=+%28b+%2B+3%29%5E2 ALIGN=MIDDLE  ALT=\"+b%5E2+%2B+%285b+-+3%29%5E2+=+%28b+%2B+3%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=26b%5E2+-+30b+%2B9+=+b%5E2+%2B+6b+%2B9 ALIGN=MIDDLE  ALT=\"26b%5E2+-+30b+%2B9+=+b%5E2+%2B+6b+%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25b%5E2+-36b=0 ALIGN=MIDDLE  ALT=\"25b%5E2+-36b=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25b%28b-36%2F25%29=0 ALIGN=MIDDLE  ALT=\"25b%28b-36%2F25%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=0 ALIGN=MIDDLE  ALT=\"b=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > makes no triangle, it must be<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28b=36%2F25%29 ALIGN=MIDDLE  ALT=\"highlight%28b=36%2F25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >cm, or, if you prefer <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28b=1.44%29 ALIGN=MIDDLE  ALT=\"highlight%28b=1.44%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >cm.<BR>\n" );
document.write( " <BR>\n" );
document.write( "You made the hypotenuse 3 cm longer than 5 times the shorter leg in<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2+%2B+%285b+-+3%29%5E2+=+%285b+%2B+3%29%5E2 ALIGN=MIDDLE  ALT=\"b%5E2+%2B+%285b+-+3%29%5E2+=+%285b+%2B+3%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "If that was really what the problem stated, then<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=26b%5E2-30b%2B9=25b%5E2%2B30b%2B9 ALIGN=MIDDLE  ALT=\"26b%5E2-30b%2B9=25b%5E2%2B30b%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-60b=0 ALIGN=MIDDLE  ALT=\"b%5E2-60b=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%28b-60%29=0 ALIGN=MIDDLE  ALT=\"b%28b-60%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and the solution would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28b=60%29 ALIGN=MIDDLE  ALT=\"highlight%28b=60%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >cm. </SPAN>\n" );
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