document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=447811>Question 447811</A>: <I><SPAN STYLE=\"word-break: break-all;\"> explanation of why an isosceles right triangles perimeter cannot be a whole number? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #308238 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=308238\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> That statement is not true; it is possible for the perimeter of an isosceles triangle to be a whole number.\r<BR>\n" );
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document.write( "Suppose the sides are <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?x\">, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?x\">, and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?x \sqrt{2}\">, where x is any positive number. The perimeter is therefore\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE P = 2x + x \sqrt{2} = x(2 + \sqrt{2})\">.\r<BR>\n" );
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document.write( "Suppose <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x = \frac{5}{2 + \sqrt{2}}\">. If we assume such a value of x, then the perimeter would be\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE P = \frac{5}{2 + \sqrt{2}} (2 + \sqrt{2}) = 5\">, which is an integer. In fact, we can replace the 5 in the numerator of x with any integer to obtain an integer perimeter.\r<BR>\n" );
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document.write( "However, if the side length itself was an integer, then it would be impossible. Proving this simply relies on the fact that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sqrt{2}\"> is irrational and cannot be multiplied by any rational number to obtain a rational number. </SPAN>\n" );
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