document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=651402>Question 651402</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The lengths of the sides of a right triangle are such that the shortest side is 7 inches shorter than the middle side, while the longest side (hypotenuse) is 1 in. longer than the middle side. Find the lengths of the sides.\r<BR>\n" );
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document.write( "I know to use A sq. + b sq. = c sq. <BR>\n" );
document.write( "a= x-7 sq<BR>\n" );
document.write( "b= x sq <BR>\n" );
document.write( "c= x+1 sq\r<BR>\n" );
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document.write( "I think I would also use sq. binomial rule as well. But I just can't get it to work. \r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #407655 by </B><A HREF=/tutors/aboutme.mpl?userid=MathTherapy><B>MathTherapy(10552)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathTherapy><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=MathTherapy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=407655\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The lengths of the sides of a right triangle are such that the shortest side is 7 inches shorter than the middle side, while the longest side (hypotenuse) is 1 in. longer than the middle side. Find the lengths of the sides.\r<BR>\n" );
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document.write( "I know to use A sq. + b sq. = c sq. <BR>\n" );
document.write( "a= x-7 sq<BR>\n" );
document.write( "b= x sq <BR>\n" );
document.write( "c= x+1 sq\r<BR>\n" );
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document.write( "I think I would also use sq. binomial rule as well. But I just can't get it to work. \r<BR>\n" );
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document.write( "Let the length of the middle side be M<BR>\n" );
document.write( "Then length of shortest side = M - 7<BR>\n" );
document.write( "Length of longest side (hypotenuse) = M + 1\r<BR>\n" );
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document.write( "Using pythagorean theorem formula, <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;\" >, where a and b are the lengths of the legs, and c is the length of the hypotenuse, we get: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=M%5E2+%2B+%28M+-+7%29%5E2+=+%28M+%2B+1%29%5E2 ALIGN=MIDDLE  ALT=\"M%5E2+%2B+%28M+-+7%29%5E2+=+%28M+%2B+1%29%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=M%5E2+%2B+M%5E2+-+14M+%2B+49+=+M%5E2+%2B+2M+%2B+1 ALIGN=MIDDLE  ALT=\"M%5E2+%2B+M%5E2+-+14M+%2B+49+=+M%5E2+%2B+2M+%2B+1\"   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=M%5E2+%2B+M%5E2+-+M%5E2+-+14M+-+2M+%2B+49+-+1+=+0 ALIGN=MIDDLE  ALT=\"M%5E2+%2B+M%5E2+-+M%5E2+-+14M+-+2M+%2B+49+-+1+=+0\"   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=M%5E2+-+16M+%2B+48+=+0 ALIGN=MIDDLE  ALT=\"M%5E2+-+16M+%2B+48+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "(M - 4)(M - 12) = 0\r<BR>\n" );
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document.write( "M, or middle side = 4  in. (ignore as this would make shortest side, - 3 (4 - 7), and length CANNOT be negative\r<BR>\n" );
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document.write( "M, or length of middle side = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%2812%29 ALIGN=MIDDLE  ALT=\"highlight_green%2812%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > in.\r<BR>\n" );
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document.write( "Length of shortest side = 12 - 7, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%285%29 ALIGN=MIDDLE  ALT=\"highlight_green%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > in.\r<BR>\n" );
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document.write( "Length of longest side = 12 + 1, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%2813%29 ALIGN=MIDDLE  ALT=\"highlight_green%2813%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > in.\r<BR>\n" );
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document.write( "This is actually one of the special right triangles, or a pythagorean triple.\r<BR>\n" );
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document.write( "Send comments and “thank-yous” to “D” at MathMadEzy@aol.com  </SPAN>\n" );
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