document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=534102>Question 534102</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this problem I am completely lost on both the setup and solving: Joe Schmoo just moved into a new house where the living room is a square whose diagonal is 7 feet longer that the length of a side.  Find the dimensions of the living room. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #351291 by </B><A HREF=/tutors/aboutme.mpl?userid=fcabanski><B>fcabanski(1391)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=fcabanski><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=351291\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Call the side of the square (living room) S.\r<BR>\n" );
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document.write( "The diagonal, D, is 7 feet longer than the length of a side.  Thus:\r<BR>\n" );
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document.write( "D = S+7\r<BR>\n" );
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document.write( "We also know a relationship between the diagonal of a square and the sides, thanks to the Pythagorean Theorem.  In simple form it's the formula for the diagonal of a square:\r<BR>\n" );
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document.write( "d = sqrt(2)*s  in our case D = sqrt(2)*S\r<BR>\n" );
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document.write( "In our case we have two equations, and two unknowns.  We can easily solve for both unknowns.  And we already have D expressed as S.  We can substitute that (S+7) in for D in the diagonal formula.\r<BR>\n" );
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document.write( "S+7 = sqrt(2)*S  Subtract S from both sides.\r<BR>\n" );
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document.write( "7 = SQRT(2)*S - S = S *((sqrt(2)-1)\r<BR>\n" );
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document.write( "Divide both sides by sqrt(2)-1\r<BR>\n" );
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document.write( "7/(sqrt(2)-1) = S = approximately 17\r<BR>\n" );
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document.write( "The room is a square with sides length 17 (approximately).\r<BR>\n" );
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document.write( "It is exactly a square with sides 7/(sqrt(2)-1) \r<BR>\n" );
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document.write( " </SPAN>\n" );
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