document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1200737>Question 1200737</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Five centimeters are cut off (along one side of) of a square sheet of paper and 8 cm are added to the adjacent side. The resulting rectangular sheet of paper has a perimeter of 98 cm.\r<BR>\n" );
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document.write( "a) What was the area of the original square piece of paper? <BR>\n" );
document.write( "b) What is the length of the diagonal of the resulting rectangular piece of paper? \r<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 #834939 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=834939\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let the sides of the squar be equal to x.<BR>\n" );
document.write( "if you take 5 cm off one side, then that side is equal to x - 5.<BR>\n" );
document.write( "if you add 8 cm to the other side, then that side is equal to x + 8.<BR>\n" );
document.write( "the resulting rectangle has two sides that are x - 5 and two sides that are x + 8.<BR>\n" );
document.write( "the resulting permieter is equal to 2 * (x - 5) + 2 * (x + 8).<BR>\n" );
document.write( "simplify to get  2x - 10 + 2x + 16<BR>\n" );
document.write( "combine like terms to get 4x + 6<BR>\n" );
document.write( "that is the perimeter.<BR>\n" );
document.write( "since the perimeter is equal to 98, you get 4x + 6 = 98<BR>\n" );
document.write( "subtract 6 from voth sides of the equation to get 4x = 92<BR>\n" );
document.write( "solve for x to get x = 92/4 = 23.<BR>\n" );
document.write( "the area of the original square is x^2 = 23^2 = 529 square cm.<BR>\n" );
document.write( "the resulting rectangle is 23 - 5 by 23 + 8 = 18 by 31.<BR>\n" );
document.write( "the diagonals form a right triangle with a height of 31 and a base of 18.<BR>\n" );
document.write( "the diagonal is the hypotenuse of this right triangle.<BR>\n" );
document.write( "the length of the diagonal is equal to sqrt(18^2 + 31^2) = sqrt(1285).<BR>\n" );
document.write( "this is equal to 35.84689666 </SPAN>\n" );
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