document.write( "Question 399108: John and Chris Maney have designed a new in-ground swimming pool for their backyard. The pool is rectangular and measures 30 feet by 20 feet. They have also designed a tile border to go around the pool. The tile border covers 216 square feet in area. What is the width x of this tile border? \n" ); document.write( "

Algebra.Com's Answer #282728 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

You can put this solution on YOUR website!
John and Chris Maney have designed a new in-ground swimming pool for their backyard.
\n" ); document.write( " The pool is rectangular and measures 30 feet by 20 feet.
\n" ); document.write( " They have also designed a tile border to go around the pool.
\n" ); document.write( " The tile border covers 216 square feet in area.
\n" ); document.write( " What is the width x of this tile border?
\n" ); document.write( ":
\n" ); document.write( "Find the area of the pool: 30 * 20 = 600 sq/ft
\n" ); document.write( "Find the overall area (A) which includes the border:
\n" ); document.write( "(2x+30)(2x+20)
\n" ); document.write( "FOIL
\n" ); document.write( "A = 4x^2 + 40x + 60x + 600
\n" ); document.write( "A = 4x^2 + 100x + 600; the overall area
\n" ); document.write( ":
\n" ); document.write( "Overall area - pool area = 216
\n" ); document.write( "4x^2 + 100x + 600 - 600 = 216
\n" ); document.write( "A quadratic equation
\n" ); document.write( "4x^2 + 100x - 216 = 0
\n" ); document.write( "Simplify, divide by 4
\n" ); document.write( "x^2 + 25x - 54 = 0
\n" ); document.write( "Factors to:
\n" ); document.write( "(x-2)(x+27) = 0
\n" ); document.write( "the positive solution
\n" ); document.write( "x = 2 ft is the width of the border
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Check this, overall dimensions would be 24 by 34, find the area:
\n" ); document.write( "24 * 34 = 816
\n" ); document.write( "Subtract the pool area (600) and you have the given area of 216
\n" ); document.write( " \n" ); document.write( "

\n" );