document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=726772>Question 726772</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please show me how to solve this word problem:\r<BR>\n" );
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document.write( "The width of a rectangular parking lot is 53ft less than its length.  Determine the dimensions of the parking lot if it measures 220ft diagonally.<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 #444789 by </B><A HREF=/tutors/aboutme.mpl?userid=DrBeeee><B>DrBeeee(684)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=DrBeeee><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=444789\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let w = the width of the driveway.<BR>\n" );
document.write( "Let l = the length of the driveway.<BR>\n" );
document.write( "Let d = the diagonal of the driveway.<BR>\n" );
document.write( "The diagonal of a rectangle is the hypotenuse of the right triangle with legs equal to length and width.<BR>\n" );
document.write( "We are given that <BR>\n" );
document.write( "(1) l = w + 53 and<BR>\n" );
document.write( "(2) d = 220<BR>\n" );
document.write( "Applying the Pythagorean theorem yields<BR>\n" );
document.write( "(3) d^2 = l^2 + w^2 or<BR>\n" );
document.write( "(4) 220^2 = (w+53)^2 + w^2 or<BR>\n" );
document.write( "(5) w^2 + 106w + 53^2 + w^2 - 220^2 = 0 or<BR>\n" );
document.write( "(6) 2w^2 + 106w - 45591 = 0 or<BR>\n" );
document.write( "(7) w^2 + 53w - 45591/2 = 0<BR>\n" );
document.write( "Using the positive square root in the quadratic equation gives us<BR>\n" );
document.write( "(8) w = (-53 + sqrt(53^2 + 2*45591))/2 or<BR>\n" );
document.write( "(9) w = (-53 + sqrt(2809 + 91182)/2 or<BR>\n" );
document.write( "(10) w = (-53 + sqrt(93991)/2 or<BR>\n" );
document.write( "(11) w = (-53 + 306.579...)/2 or<BR>\n" );
document.write( "(12) w = (253.579...)/2 or<BR>\n" );
document.write( "(13) w = 126.789...<BR>\n" );
document.write( "Then using (1) we get<BR>\n" );
document.write( "(14) l = 179.789...<BR>\n" );
document.write( "Let's check w and l using (3).<BR>\n" );
document.write( "Is (220^2 = (179.789...)^2 + (126.789...)^2)?<BR>\n" );
document.write( "Is (220^2 = 32324.357... + 16075.643...)?<BR>\n" );
document.write( "Is (48400 = 48400)? Yes<BR>\n" );
document.write( "Answer: The parking lot is 179.789... ft by 126.789... ft.<BR>\n" );
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