document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=981574>Question 981574</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1. A new square is formed by joining the midpoints of the consecutive<BR>\n" );
document.write( "sides of a square 8 inches on a side. If the process is continued until<BR>\n" );
document.write( "there are already six squares, find the sum of the areas of all squares<BR>\n" );
document.write( "in square inches. \r<BR>\n" );
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document.write( "2.In President Sergio Osmeña High School, suspension of classes is<BR>\n" );
document.write( "announced through text brigade. One stormy day, the principal<BR>\n" );
document.write( "announces the suspension of classes to two teachers, each of whom<BR>\n" );
document.write( "sends this message to two other teachers, and so on. Suppose that<BR>\n" );
document.write( "text messages were sent in five rounds, counting the principal’s text<BR>\n" );
document.write( "message as the first, how many text messages were sent in all? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #602548 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=602548\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "Consider a square with sides that measure <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\">.  If you create a new square by joining the midpoints of the adjacent sides, the side of the new square will be the hypotenuse of an isosceles right triangle with legs that measure <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{x}{2}\">, from which it is a simple application of the Pythagorean Theorem to determine that the measure of the side of the new square is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{x\sqrt{2}}{2}\">.  From that you can see that the area of the new square is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{x^2}{2}\">, exactly half of the area of the original square.\r<BR>\n" );
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document.write( "Your original square is 8 by 8 or 64 square inches.  The next one is half of that or 32 square inches, and so on...\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\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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