document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=388129>Question 388129</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 3 squares with the first square's side length is 4 units, the next one to the right has side length of x units and the next square to the right has side length of 9 units. there is a straight line which's coordinates lies on the topleft vertices of each 3 squares.\r<BR>\n" );
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document.write( "=> what is the side length of the middle square? <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #274824 by </B><A HREF=/tutors/aboutme.mpl?userid=CharlesG2><B>CharlesG2(834)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CharlesG2><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=274824\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 3 squares with the first square's side length is 4 units, the next one to the right has side length of x units and the next square to the right has side length of 9 units. there is a straight line which's coordinates lies on the topleft vertices of each 3 squares.\r<BR>\n" );
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document.write( "=> what is the side length of the middle square? \r<BR>\n" );
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document.write( "a vertex is one of the corners of one of the squares,<BR>\n" );
document.write( "vertices is plural of vertex<BR>\n" );
document.write( "set lower left corner of first square on origin (0,0)<BR>\n" );
document.write( "top left corner first square: (0,4)<BR>\n" );
document.write( "top left corner 2nd square: (4,x)<BR>\n" );
document.write( "top left corner 3rd square: (4 + x,9)<BR>\n" );
document.write( "slope = rise/run = (y2 - y1)/(x2 - x1)<BR>\n" );
document.write( "slope between (0,4) and (4,x) --> (x - 4)/(4 - 0) = (x - 4)/4<BR>\n" );
document.write( "slope between (4,x) and (4 + x,9) --> (9 - x)/(4 + x - 4) = (9 - x)/x<BR>\n" );
document.write( "2 slopes need to be equal<BR>\n" );
document.write( "(x - 4)/4 = (9 - x)/x<BR>\n" );
document.write( "x(x - 4)/4 = (9 - x)<BR>\n" );
document.write( "x(x - 4) = (9 - x)4<BR>\n" );
document.write( "x^2 - 4x = 36 - 4x<BR>\n" );
document.write( "x^2 - 4x + 4x - 36 = 0<BR>\n" );
document.write( "x^2 - 36 = 0<BR>\n" );
document.write( "(x + 6)(x - 6) = 0<BR>\n" );
document.write( "x can not be -6<BR>\n" );
document.write( "x = 6<BR>\n" );
document.write( "side length is 6<BR>\n" );
document.write( "check:<BR>\n" );
document.write( "(x - 4)/4 = (6 - 4)/4 = 2/4 = 1/2<BR>\n" );
document.write( "(9 - x)/x = (9 - 6)/6 = 3/6 = 1/2, same so yes<BR>\n" );
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