document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=419199>Question 419199</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 6. In the two squares shown below, the longer square has a side length 1 foot greater than that of the<BR>\n" );
document.write( "smaller square. If the combined area of the two squares is 113 square feet, find the length of the<BR>\n" );
document.write( "side of the smaller square. (Define any variables that you use by using let statements and/or by<BR>\n" );
document.write( "labeling the diagram.) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #293236 by </B><A HREF=/tutors/aboutme.mpl?userid=duckness73><B>duckness73(47)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=duckness73><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=duckness73><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=293236\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x = length of the side of the small square.  This means that:<BR>\n" );
document.write( "x + 1 = length of the side of the large square.\r<BR>\n" );
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document.write( "The area of the small square is x^2<BR>\n" );
document.write( "The area of the large square is (x + 1) ^ 2\r<BR>\n" );
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document.write( "Since the combined area of the two squares is 113, we have\r<BR>\n" );
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document.write( "x^2 + ((x + 1) ^ 2) = 113<BR>\n" );
document.write( "x^2 + (x^2 + 2x + 1) = 113  (expanding the expression)<BR>\n" );
document.write( "2x^2 + 2x + 1 = 113   (combining like terms)<BR>\n" );
document.write( "2x^2 + 2x - 112 = 0  (subtracting 113 from both sides)<BR>\n" );
document.write( "x^2 + x - 56 = 0 (dividing both sides by 2)<BR>\n" );
document.write( "(x - 7)(x + 8) = 0  (factoring)<BR>\n" );
document.write( "x = 7  or x = -8  (setting each factor to zero and solving)\r<BR>\n" );
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document.write( "So, the side of the small square is either 7 or -8.  Since it doesn't make sense for a square to have a side -8 units long, the side of the small square is 7.\r<BR>\n" );
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document.write( "Answer: the length of the side of the small square is 7.  (And, BTW, the length of the side of the large square is x + 1 = 7 + 1 = 8). </SPAN>\n" );
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