document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=534076>Question 534076</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Sum of the ares of 2 square is 468 msquare. If the difference of their perimeter is 24m. Find the sides of 2 square. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #351273 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=351273\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Call S = sides of square 1 (square S).  We'll make this one the square with the larger perimeter.<BR>\n" );
document.write( "Call T = sides of square 2 (square T)\r<BR>\n" );
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document.write( "The perimeter of square 1 is S + S + S + S = 4S.  The area of square 1 is S^2\r<BR>\n" );
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document.write( "The perimeter of square 2 is T + T + T + T = 4T.  The area of square 2 is T^2\r<BR>\n" );
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document.write( "We called S the square with the larger perimeter, and we know the difference is 24, so:\r<BR>\n" );
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document.write( "4S = 4T + 24\r<BR>\n" );
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document.write( "We know the sum of their areas is 468.  \r<BR>\n" );
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document.write( "S^2 + T^2 = 468\r<BR>\n" );
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document.write( "Two equations, two unknowns.  So let's solve the first equation for S in terms of T.\r<BR>\n" );
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document.write( "4S = 4T + 24  divide both sides by 4 --->  S = 4T/4 + 24 = T+6\r<BR>\n" );
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document.write( "Substitute that for S in the area equation, so we can solve it for T.\r<BR>\n" );
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document.write( "S^2 + T^2 = 468  (substitute T+6 for S)\r<BR>\n" );
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document.write( "(T+6)^2 + T^2 = 468  Use FOIL to square T+6\r<BR>\n" );
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document.write( "T^2 + 12T + 36 +T^2 = 468  Combine the T^2 terms, subtract 468 from each side.\r<BR>\n" );
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document.write( "2T^2 + 12T - 432 = 0\r<BR>\n" );
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document.write( "Factor 2 from each term.\r<BR>\n" );
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document.write( "T^2 + 6T - 216 = 0  Factor using reverse FOIL.\r<BR>\n" );
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document.write( "(T+18)(T-12)  solve each for T\r<BR>\n" );
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document.write( "T+18=0  (subtract 18 from each side)  T=-18  This solution is valid, but not in the real world because the side of a square can't be a negative number.\r<BR>\n" );
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document.write( "T-12=0  (add 12 to both sides)  T = 12\r<BR>\n" );
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document.write( "Sides of T = 12.  It's perimeter is 4*12 = 48m\r<BR>\n" );
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document.write( "Remember earlier we found that S = T+6 = 12 + 6 = 18.  Thus the perimeter of S is 4*18 = 72m\r<BR>\n" );
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document.write( "Now check if these are the correct answers.\r<BR>\n" );
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document.write( "The perimeter of S should be 24m more than the perimeter of T.\r<BR>\n" );
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document.write( "72-48 = 24  CHECK\r<BR>\n" );
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document.write( "The combined areas should be 468 m^2.\r<BR>\n" );
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document.write( "12^2 + 18^2 = 144+324 = 468  CHECK\r<BR>\n" );
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document.write( "HURRAH...we found the answer.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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