document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=168149>Question 168149</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This one has been answered but the answer does not make sense.  I emailed the tutor and have not heard back.  Will someone please take a look at this for me?<BR>\n" );
document.write( "Thanks\r<BR>\n" );
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document.write( "A square mat has a uniform red border on all four sides.  The rest of the mat is blue.  The width of the blue square is three-fourths the width of the entire square.  If the area colored red is 28 m squared, determine the lengths of each side of the mat. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #123916 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><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=123916\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let:<BR>\n" );
document.write( "W1 = width of the large square.<BR>\n" );
document.write( "L1 = length of the large square.<BR>\n" );
document.write( "W2 = width of the large square.<BR>\n" );
document.write( "L2 = length of the large square.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "you are given that w = the width of the large square:<BR>\n" );
document.write( "W1 = w<BR>\n" );
document.write( "since this is a square, then L1 = w also.<BR>\n" );
document.write( "you have:<BR>\n" );
document.write( "L1 = W1 = w<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "you are given that .75*w = the width of the small square:<BR>\n" );
document.write( "W2 = .75*w<BR>\n" );
document.write( "since this is a square, then L2 = .75*w also.<BR>\n" );
document.write( "you have:<BR>\n" );
document.write( "L2 = W2 = .75*w<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "area of the large square is L1*W1 = A1<BR>\n" );
document.write( "area of the small square is L2*W2 = A2<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "large square is all red (assumed since you are only given that the border is red).<BR>\n" );
document.write( "small square is all blue (given).<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "if you take the small square and put it in the middle of and on top of the large square, what you will have is a blue square in the middle with a red border.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "that, i believe, is what causes your problem to be solved as follows:<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "you are given that the red border is 28 square meters.<BR>\n" );
document.write( "if you take the area of the large square and subtract the area of the small square you will be left with the area of the border.<BR>\n" );
document.write( "so, your equation is:<BR>\n" );
document.write( "A1 - A2 = 28<BR>\n" );
document.write( "since A1 = L1*W1, and A2 = L2*W2, this becomes:<BR>\n" );
document.write( "L1*W1 - L2*W2 = 28<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "since L1 = w, and W1 = w, this becomes:<BR>\n" );
document.write( "w*w - L2*W2 = 28<BR>\n" );
document.write( "since L2 = .75*w, and W2 = .75*w, this becomes:<BR>\n" );
document.write( "w*w - (.75*w)*(.75*w) = 28<BR>\n" );
document.write( "simplifying:<BR>\n" );
document.write( "w^2 - .5625*w^2 = 28<BR>\n" );
document.write( "(1-.5625)*w^2 = 28<BR>\n" );
document.write( ".4375*w^2 = 28<BR>\n" );
document.write( "w^2 = 28/.4375<BR>\n" );
document.write( "w^2 = 64<BR>\n" );
document.write( "w = 8<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "if w = 8, then .75*w = 6<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "since w = 8, then<BR>\n" );
document.write( "L1 = 8<BR>\n" );
document.write( "W1 = 8<BR>\n" );
document.write( "since .75*w = 6, then<BR>\n" );
document.write( "L2 = 6<BR>\n" );
document.write( "W2 = 6<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "your original equation is:<BR>\n" );
document.write( "L1*W1 - L2*W2 = 28<BR>\n" );
document.write( "this becomes:<BR>\n" );
document.write( "8*8 - 6*6 = 28<BR>\n" );
document.write( "this becomes:<BR>\n" );
document.write( "64 - 36 = 28<BR>\n" );
document.write( "which becomes:<BR>\n" );
document.write( "28 = 28<BR>\n" );
document.write( "since this statement is true, the value for w = 8 is correct.<BR>\n" );
document.write( "the lengths of each side of the mat are:<BR>\n" );
document.write( "8 inches for the large square.<BR>\n" );
document.write( "6 inches for the small square.<BR>\n" );
document.write( "-----\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );