document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=114986>Question 114986</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Carpentry:<BR>\n" );
document.write( "The perimeter of the rectangular window is 14 ft. and its length is 2 ft less than twice the width.  What are the dimensions of the window? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #83654 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=83654\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The perimeter of a plane figure is the sum of the lengths of its sides. Since you are told<BR>\n" );
document.write( "that the figure is a rectangle you know that its sides are its length (call it L) and its<BR>\n" );
document.write( "width (call it W) and by the definition of a rectangle there are two lengths and two widths.<BR>\n" );
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document.write( "Therefore, you can write an equation for the perimeter (call it P) as:<BR>\n" );
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document.write( "P = 2L + 2W<BR>\n" );
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document.write( "And since you are told that the perimeter is 14 feet, you can substitute 14 for P to make<BR>\n" );
document.write( "the equation become:<BR>\n" );
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document.write( "14 = 2L + 2W<BR>\n" );
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document.write( "Next you are told that its length is 2 feet less than twice its width. If the length equaled <BR>\n" );
document.write( "twice its width you could say L = 2W, but the length is 2 feet less than 2W. So you can<BR>\n" );
document.write( "write this equation as:<BR>\n" );
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document.write( "L = 2W - 2<BR>\n" );
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document.write( "Now you can return to the perimeter equation and substitute 2W - 2 for L because they are<BR>\n" );
document.write( "equals. The perimeter equation is:<BR>\n" );
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document.write( "14 = 2L + 2W<BR>\n" );
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document.write( "Replace L with the quantity 2W - 2 and this equation becomes:<BR>\n" );
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document.write( "14 = 2(2W - 2) + 2W<BR>\n" );
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document.write( "Multiply out the first term on the right side of this equation and the equation becomes:<BR>\n" );
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document.write( "14 = 4W - 4 + 2W<BR>\n" );
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document.write( "On the right side combine the 4W and the +2W to get 6W and the equation then is:<BR>\n" );
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document.write( "14 = 6W - 4<BR>\n" );
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document.write( "Get rid of the -4 on the right side by adding +4 to both sides of the equation and the<BR>\n" );
document.write( "equation then is:<BR>\n" );
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document.write( "18 = 6W<BR>\n" );
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document.write( "Solve for W by dividing both sides of the equation by 6 and you have:<BR>\n" );
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document.write( "3 = W<BR>\n" );
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document.write( "So W is 3 feet. Since there are two widths in the rectangle, the combined widths are 6<BR>\n" );
document.write( "feet. Take that away from the perimeter and you have 14 - 6 = 8 feet. This remaining<BR>\n" );
document.write( "8 feet is the dimension for the two lengths of the rectangle. So each length must be<BR>\n" );
document.write( "half of 8 feet ... or you can say that the length of the window is 8 divided by 2 and this<BR>\n" );
document.write( "is 4 feet.<BR>\n" );
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document.write( "In summary, the width of the window is 3 feet and the length of the window is 4 feet.<BR>\n" );
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document.write( "Check: The perimeter of the window is to be 14 feet. Add up the lengths and the widths:<BR>\n" );
document.write( "4 + 4 + 3 + 3 and the sum is 14. So that requirement checks.<BR>\n" );
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document.write( "Next the length is to be 2 feet less than twice the width. Twice the width is 2 times 3<BR>\n" );
document.write( "which is 6 feet. Is the length (4 feet) 2 feet less than 6 feet. Yes, it is. So the answers<BR>\n" );
document.write( "check out.<BR>\n" );
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document.write( "Hope this helps you to see your way through the problem.<BR>\n" );
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