document.write( "Question 1166543: A farmer has a 100foot by 25 foot rectangular field that he wants to reduce to 16% of its original size. How wide of a strip should he cut around the edge of his field to do this? \n" ); document.write( "

Algebra.Com's Answer #791072 by htmentor(1343) $\"\"$ $\"About$

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Let l, w be the length and width of the lawn. Let s = the strip width.
\n" ); document.write( "The length of the rectangle remaining to mow is l - 2s, since it's reduced by s on either side
\n" ); document.write( "Similarly, the width remaining to mow is w - 2s
\n" ); document.write( "The new area is 16% of the original area:
\n" ); document.write( "A1 = 0.16*l*w = 0.16*100*25 = 400 = (l-2s)(w-2s)
\n" ); document.write( "(100-2s)(25-2s) = 400
\n" ); document.write( "2500 - 200s - 50s + 4s^2 - 400 = 0
\n" ); document.write( "4s^2 - 250s + 2100 = 0
\n" ); document.write( "2s^2 - 125s + 1050 = 0
\n" ); document.write( "This can be factored as: (2s-105)(s-10) = 0
\n" ); document.write( "The first solution gives a strip wider than the width of the lawn, so we take
\n" ); document.write( "the 2nd: s=10
\n" ); document.write( "A 10 ft wide strip will leave 16% of the original area
\n" ); document.write( "Check: (100-20)(25-20) = 80*5 = 400\r
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