document.write( "Question 269238: A cement walk of uniform width is built around a 20 foot by 40 foot rectangular pool and the area of the walk is 700 square feet. How wide will the walk be? \n" ); document.write( "

Algebra.Com's Answer #197324 by dabanfield(803) $\"\"$ $\"About$

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A cement walk of uniform width is built around a 20 foot by 40 foot rectangular pool and the area of the walk is 700 square feet. How wide will the walk be?\r
\n" ); document.write( "\n" ); document.write( "Let x be the uniform width of the walk. Then the length and width of the rectangle bounded by the outer edge of the walk are 40+2x and 20+2x respectively. The area of the walk is the total area of the outer rectangle minus the area of the pool or:\r
\n" ); document.write( "\n" ); document.write( "(20+2x)*(40+2x) - 20*40 = 700\r
\n" ); document.write( "\n" ); document.write( "40*20 + 40x + 80x + 4x^2 - 800 = 700
\n" ); document.write( "800 +120x + 4x^2 - 800 = 700
\n" ); document.write( "4x^2 + 120x - 700 = 0\r
\n" ); document.write( "\n" ); document.write( "Divide both sides by 4:\r
\n" ); document.write( "\n" ); document.write( "x^2 + 30x - 175 = 0\r
\n" ); document.write( "\n" ); document.write( "Factor the above:\r
\n" ); document.write( "\n" ); document.write( "(x+35)*(x-5) = 0 \r
\n" ); document.write( "\n" ); document.write( "The solution for x must satisfy either x+35 = 0 and/or x-5 = 0\r
\n" ); document.write( "\n" ); document.write( "These solutions are x = -35 and x = 5. Since the width must be positive, the correct value for x must be 5. \n" ); document.write( "

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