document.write( "Question 836017: A rectangular lawn measures 60ft. by 80ft. Part of the lawn is torn up to install a sidewalk of uniform width around it. The area of the new lawn is $\"2400ft%5E2\"$ . How wide is the sidewalk? \n" ); document.write( "

Algebra.Com's Answer #503923 by josgarithmetic(39617) $\"\"$ $\"About$

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New area of the lawn becomes $\"%2860-2w%29%2880-2w%29=2400\"$ , using w as the width of the sidewalk.\r
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\n" ); document.write( "\n" ); document.write( " $\"4%2830-w%29%2840-w%29=4%2A600\"$
\n" ); document.write( " $\"%2830-w%29%2840-w%29=600\"$
\n" ); document.write( " $\"1200-70w%2Bw%5E2=600\"$
\n" ); document.write( " $\"600-70w%2Bw%5E2=0\"$ \r
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\n" ); document.write( "\n" ); document.write( "Try to factor the quadratic expression.
\n" ); document.write( "600=100*2*3=2*5*2*5*2*3=2*2*2*3*5*5,,,, if seems too much trouble, just use general solution for a quadratic formula.\r
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\n" ); document.write( "\n" ); document.write( "Discrim, 70^2-4*600=4900-2400=2500
\n" ); document.write( " $\"w=%2870%2B-+sqrt%282500%29%29%2F%282%29\"$
\n" ); document.write( " $\"w=%2870%2B-+5%2A10%29%2F2\"$ , we must use the positive value.
\n" ); document.write( " $\"highlight%28w=10%29\"$ or $\"cross%28w=60%29\"$ , only one of them making sense.\r
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\n" ); document.write( "\n" ); document.write( "Worth a check:
\n" ); document.write( "(60-2*10)(80-2*10)=2400?
\n" ); document.write( " $\"%2860-20%29%2880-20%29\"$
\n" ); document.write( " $\"40%2A60=2400\"$ yes. \n" ); document.write( "

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