document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=342101>Question 342101</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A rectangle is 3 times as long as the width and has the same perimeter as a square whose area is 4 sq. ft larger than the rectangle. what are the dimensions of the rectangle and square? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #245059 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=245059\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A rectangle is 3 times as long as the width and has the same perimeter as a<BR>\n" );
document.write( " square whose area is 4 sq. ft larger than the rectangle.<BR>\n" );
document.write( " what are the dimensions of the rectangle and square?<BR>\n" );
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document.write( "Let x = width of the rectangle<BR>\n" );
document.write( "then<BR>\n" );
document.write( "3x = the length of the rectangle<BR>\n" );
document.write( "then<BR>\n" );
document.write( "P = 2(3x) + 2x = 8x is the perimeter of the rectangle<BR>\n" );
document.write( "and<BR>\n" );
document.write( "3x * x = 3x^2 = area of the rectangle<BR>\n" );
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document.write( "Let s = side of the square<BR>\n" );
document.write( "then<BR>\n" );
document.write( "4s = the perimeter of the square<BR>\n" );
document.write( "and<BR>\n" );
document.write( "s^2 = the area of the square<BR>\n" );
document.write( ":<BR>\n" );
document.write( "the equal perimeters equation<BR>\n" );
document.write( "4s = 8x<BR>\n" );
document.write( "simplify, divide by 2<BR>\n" );
document.write( "s = 2x<BR>\n" );
document.write( ":<BR>\n" );
document.write( "That areas equation<BR>\n" );
document.write( "s^2 - 3x^2 = 4<BR>\n" );
document.write( "replace s with 2x<BR>\n" );
document.write( "(2x)^2 - 3x^2 = 4<BR>\n" );
document.write( "4x^2 - 3x^2 = 4<BR>\n" );
document.write( "x^2 = 4<BR>\n" );
document.write( "x = 2 ft is the width of the rectangle<BR>\n" );
document.write( "then<BR>\n" );
document.write( "3(2) = 6 ft is the length of the rectangle<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Find the side of the square<BR>\n" );
document.write( "s = 2(2)<BR>\n" );
document.write( "s = 4 ft is the side of the square<BR>\n" );
document.write( ":<BR>\n" );
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document.write( "Check solutions by finding the perimeter<BR>\n" );
document.write( "Rectangle: 2(6) + 2(2) = 16 ft<BR>\n" );
document.write( "Square: 4 * 4 = 16 ft<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Check the areas<BR>\n" );
document.write( "4^2 - (6*2) = 4<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );