document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=360165>Question 360165</A>: <I><SPAN STYLE=\"word-break: break-all;\"> One leg of a right triangle is 1 in. shorter than the other leg. The hypotenuse is 4 in. longer than the shorter side. Find the length of each side. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #256986 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=256986\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\"> represent the measure of the shortest leg.  Then <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ +\ 1\"> represents the measure of the other leg and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ +\ 4\"> represents the measure of the hypotenuse.\r<BR>\n" );
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document.write( "With a tip o' the hat to Mr. Pythagoras we write:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x^2\ +\ (x\ +\ 1)^2\ =\ (x\ +\ 4)^2\">\r<BR>\n" );
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document.write( "Expand the binomials:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x^2\ +\ x^2\ +\ 2x\ +\ 1\ =\ x^2\ +\ 8x\ +\ 16\">\r<BR>\n" );
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document.write( "Collect like terms in the LHS:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x^2\ -\ 6x\ -\ 15\ =\ 0\">\r<BR>\n" );
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document.write( "Solve the quadratic for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\">.  Then compute <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ +\ 1\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ +\ 4\">.\r<BR>\n" );
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document.write( "Hint #1:  This does not factor.  Use the Quadratic Formula (or complete the square if you are glutton for punishment).\r<BR>\n" );
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document.write( "Hint #2:  Since the problem doesn't give you a round-off precision, it must want the exact answer.  Hence, leave your answer in radical form.  However, you will need to estimate the numerical approximation to determine whether either of your answers are negative.  Since you are looking for a positive measure of length, you need to discard any negative root.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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