document.write( "Question 236457: A small rectangular playground that is 10 feet by 14 feet is going to have a grass border of uniform width on all sides. If the area of the grass border is 145 square feet, how wide is the border? \n" ); document.write( "

Algebra.Com's Answer #174093 by checkley77(12844) $\"\"$ $\"About$

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10*14=140 ft^2 is the playground area.
\n" ); document.write( "10 plus 2 times the border times 14 plus 2 times the border=140+145.
\n" ); document.write( "(10+2x)(14+2x)=140+145
\n" ); document.write( "140+28x+20x+4x^2=285
\n" ); document.write( "4x^2+48x+140-285=0
\n" ); document.write( "4x^2+48x-145=0
\n" ); document.write( " $\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"$
\n" ); document.write( "x=(-48+-sqrt[48^2-4*4*-145)/2*4
\n" ); document.write( "x=(-48+-sqrt[2,304+2,320)/8
\n" ); document.write( "x=(-48+-sqrt4,624)/8
\n" ); document.write( "x=(-48+-68)/8
\n" ); document.write( "x=(-48+68)/8
\n" ); document.write( "x=20/8
\n" ); document.write( "x=2.5 ft. is the width of the border.
\n" ); document.write( "Proof:
\n" ); document.write( "(10+2*2.5)(14+2*2.5)=285
\n" ); document.write( "(10+5)(14+5)=285
\n" ); document.write( "15*19=285
\n" ); document.write( "285=285 \n" ); document.write( "

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