document.write( "Question 71134: I am not sure how to set this up so I can solve it. Your help is greatly appreciated.\r
\n" ); document.write( "\n" ); document.write( "62. a 60 ft by 80 ft parking lot is torn up to install a sidewalk of uniform width around it's perimeters. The new area of the parking lot is 2/3 of the old area. How wide is the sidewalk? \n" ); document.write( "

Algebra.Com's Answer #50874 by ptaylor(2198) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let x=width of sidewalk\r
\n" ); document.write( "\n" ); document.write( "Then (60-2x) and (80-2x) would be new dimensions of parking lot\r
\n" ); document.write( "\n" ); document.write( "And (60-2x)(80-2x) would be new area of parking lot
\n" ); document.write( "Also (60)(80)=4800 sq ft= old area\r
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\n" ); document.write( "\n" ); document.write( "Now we are told that the new area is 2/3 that of the old area. So our equation to solve is:\r
\n" ); document.write( "\n" ); document.write( "(60-2x)(80-2x)=(2/3)(4800) get rid of parens
\n" ); document.write( "4800-280x+4x^2=3200 subtract 3200 from both sides\r
\n" ); document.write( "\n" ); document.write( "4800-3200-280x+4x^2=3200-3200 collect like terms:\r
\n" ); document.write( "\n" ); document.write( "4x^2-280x+1600=0 divide all terms by 4\r
\n" ); document.write( "\n" ); document.write( "x^2-70x+400=0\r
\n" ); document.write( "\n" ); document.write( "We'll solve using the quadratic formula:\r
\n" ); document.write( "\n" ); document.write( " $\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"$
\n" ); document.write( " $\"x+=+%2870+%2B-+sqrt%28+4900-1600+%29%29%2F%282%29+\"$
\n" ); document.write( " $\"x+=+%2870+%2B-+%28+57.446+%29%29%2F%282%29+\"$
\n" ); document.write( "x =6.277 ft------------------------------correct ans
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\n" ); document.write( "x=63.723 ft--------------------------------impossible ans\r
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\n" ); document.write( "\n" ); document.write( "CK\r
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\n" ); document.write( "\n" ); document.write( "2x=2(6.277)=12.554\r
\n" ); document.write( "\n" ); document.write( "(60-12.554)(80-12.554)=3200\r
\n" ); document.write( "\n" ); document.write( "(47.446)(67.446)=3200\r
\n" ); document.write( "\n" ); document.write( "3200=3200\r
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