document.write( "Question 1115712: A club swimming pool is 24
\n" ); document.write( "
\n" ); document.write( "ft wide and 40
\n" ); document.write( "
\n" ); document.write( "ft long. The club members want an exposed aggregate border in a strip of uniform width around the pool. They have enough material for 576
\n" ); document.write( "
\n" ); document.write( "ft squared
\n" ); document.write( ".
\n" ); document.write( "How wide can the strip​ be? \n" ); document.write( "
Algebra.Com's Answer #730547 by ikleyn(52790)\"\" \"About 
You can put this solution on YOUR website!
.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "         * * * This absolutely standard problem on quadratic equation application was solved in this forum at least 100 times. * * *\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\r\n" );
document.write( "The larger rectangle dimensions are (24+2*x) feet and (40+2*x) feet.\r\n" );
document.write( "\r\n" );
document.write( "The larger rectangle area is the product of its dimensions  (24+2*x)*(40+2*x) square feet.\r\n" );
document.write( "\r\n" );
document.write( "The pool area is 24*40 square feet.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The area of the uniform border around the pool is the difference of the two areas  (24+2*x)*(40+2*x) - 24*40.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It is exactly  576 square feet, which gives you your governing equation\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    (24+2x)*(40+2x) - 24*40 = 576\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Simplify and solve it for x:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    2x*40 + 2x*24 + 4x^2 = 576\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    4x^2 + 128x - 576 = 0\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    x^2 + 32x - 144 = 0\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    (x-4)*(x+36) = 0\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The only positive root  x= 4 ft  is the solution.   ANSWER\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "CHECK.  (24+2*4)*(40+2*4) - 24*40 = 576.    ! Correct !\r\n" );
document.write( "
\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "===========
\n" ); document.write( "To see many other similar solved problems,  look into the lessons\r
\n" ); document.write( "\n" ); document.write( "    - Problems on the area and the dimensions of a rectangle\r
\n" ); document.write( "\n" ); document.write( "    - Problems on the area and the dimensions of a rectangle surrounded by a strip (*)\r
\n" ); document.write( "\n" ); document.write( "    - Cynthia Besch wants to buy a rug for a room (*)\r
\n" ); document.write( "\n" ); document.write( "    - Problems on a circular pool and a walkway around it\r
\n" ); document.write( "\n" ); document.write( "    - Had the dimensions of a rectangle be changed . . . \r
\n" ); document.write( "\n" ); document.write( "    - OVERVIEW of lessons on dimensions and the area of rectangles and circles and their elements\r
\n" ); document.write( "\n" ); document.write( "in this site.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The lessons marked (*) in the list are the most relevant to this problem.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );