document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=218860>Question 218860</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a right triangle has sides whose lengths are consecutive integers. Find the lengths of the sides.<BR>\n" );
document.write( "i dont know how to find the lengths of the sides. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #164730 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=164730\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First a definition: Consecutive integers are simply whole numbers that follow one another. Example: 1, 2, 3, 4, 5, 6, etc are consecutive integers.\r<BR>\n" );
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document.write( "In general, the terms x, x+1, x+2, x+3, x+4, ... are consecutive integers (where 'x' is a whole number).\r<BR>\n" );
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document.write( "Since we're given that \"a right triangle has sides whose lengths are consecutive integers\", we're basically told that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=x ALIGN=MIDDLE  ALT=\"a=x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=x%2B1 ALIGN=MIDDLE  ALT=\"b=x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=x%2B2 ALIGN=MIDDLE  ALT=\"c=x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > where 'a' and 'b' are the legs of the triangle and 'c' is the hypotenuse.\r<BR>\n" );
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document.write( "Now remember that we can relate the sides of a triangle using the Pythagorean theorem: <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( "Just plug in the values of 'a', 'b', and 'c' to get: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B%28x%2B1%29%5E2=%28x%2B2%29%5E2 ALIGN=MIDDLE  ALT=\"x%5E2%2B%28x%2B1%29%5E2=%28x%2B2%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=x%5E2%2Bx%5E2%2B2x%2B1=x%5E2%2B4x%2B4 ALIGN=MIDDLE  ALT=\"x%5E2%2Bx%5E2%2B2x%2B1=x%5E2%2B4x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > FOIL\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2Bx%5E2%2B2x%2B1-x%5E2-4x-4=0 ALIGN=MIDDLE  ALT=\"x%5E2%2Bx%5E2%2B2x%2B1-x%5E2-4x-4=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Get everything to one side.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-2x-3=0 ALIGN=MIDDLE  ALT=\"x%5E2-2x-3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "From here, just use the quadratic formula or factor to find 'x'. I'll let you do that. </SPAN>\n" );
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