document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1207016>Question 1207016</A>: <I><SPAN STYLE=\"word-break: break-all;\"> one leg of a right triangle is 2 cm longer than the other leg, hypotenuse is 7 cm longer than the shorter leg. find the lengths of three sides of the right triangle </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #844818 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=844818\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "a = x = shorter leg<BR>\n" );
document.write( "b = x+2 = longer leg<BR>\n" );
document.write( "c = x+7 = hypotenuse\r<BR>\n" );
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document.write( "The Pythagorean Theorem<BR>\n" );
document.write( "a^2+b^2 = c^2<BR>\n" );
document.write( "leads to<BR>\n" );
document.write( "x^2+(x+2)^2 = (x+7)^2\r<BR>\n" );
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document.write( "Expand everything out and get everything to one side to end up with this<BR>\n" );
document.write( "x^2 - 10x - 45 = 0\r<BR>\n" );
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document.write( "Use of the quadratic formula will lead to:<BR>\n" );
document.write( "x = 5 + sqrt(70) = 13.3666 or x = 5 - sqrt(70) = -3.3666<BR>\n" );
document.write( "The decimal values are approximate.<BR>\n" );
document.write( "The negative solution is tossed out since we cannot have a negative side length.\r<BR>\n" );
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document.write( "x = 13.3666 leads to,<BR>\n" );
document.write( "x+2 = 13.3666+2 = 15.3666<BR>\n" );
document.write( "x+7 = 13.3666+7 = 20.3666\r<BR>\n" );
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document.write( "<font color=red>Summary</font><BR>\n" );
document.write( "The sides of the right triangle are<BR>\n" );
document.write( "a = 13.3666 <BR>\n" );
document.write( "b = 15.3666<BR>\n" );
document.write( "c = 20.3666<BR>\n" );
document.write( "Each value is approximate.\r<BR>\n" );
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document.write( "Check:<BR>\n" );
document.write( "a^2+b^2 = c^2<BR>\n" );
document.write( "13.3666^2+15.3666^2 = 20.3666^2<BR>\n" );
document.write( "414.79839112 = 414.79839556<BR>\n" );
document.write( "The two sides aren't an exact match, but they're very close. <BR>\n" );
document.write( "We have a bit of rounding error. <BR>\n" );
document.write( "The decimal portion \"79839\" matches up at least.\r<BR>\n" );
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document.write( "Another way to check:<BR>\n" );
document.write( "a^2+b^2 = c^2<BR>\n" );
document.write( "a^2+b^2-c^2 = 0<BR>\n" );
document.write( "13.3666^2+15.3666^2-20.3666^2 = 0<BR>\n" );
document.write( "-0.00000444 = 0<BR>\n" );
document.write( "Note the first five decimal digits are 0 to indicate we have those decimal digits matching in the previous check section (the \"79839\" portion).<BR>\n" );
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