document.write( "Question 743087: the area of a rectangular plot 30 feet long and 20 feet wide will be doubled by creating a border around the plot. what width should the border be to accomplish this? \n" ); document.write( "

Algebra.Com's Answer #452759 by davethejackal(28) $\"\"$ $\"About$

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Let b = width of the border\r
\n" ); document.write( "\n" ); document.write( "Current area of the rectangle = 20 x 30 = 600 sq ft \r
\n" ); document.write( "\n" ); document.write( "By adding the border on either side of the rectangle its length will be increased by b on one side and b on the other side and so the length becomes 30+2b.\r
\n" ); document.write( "\n" ); document.write( "Similarly the width becomes 20+2b\r
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\n" ); document.write( "\n" ); document.write( "Area of the rectangle with the border = width x length = (20+2b)(30+2b) [1]\r
\n" ); document.write( "\n" ); document.write( "We are told this = twice the original area = twice 600 sq ft = 1200 sq ft\r
\n" ); document.write( "\n" ); document.write( "Hence $\"+%2820%2B2b%29%2830%2B2b%29+=+1200+\"$ \r
\n" ); document.write( "\n" ); document.write( "Multiplying this out gives $\"+600+%2B+20x2b+%2B+30x2b+%2B+4b%5E2+=+600+\"$ \r
\n" ); document.write( "\n" ); document.write( "Subtracting 600 from both sides and simplifying gives:
\n" ); document.write( " $\"+4b%5E2+%2B+100b+-600+=+0++\"$ \r
\n" ); document.write( "\n" ); document.write( "Factorising gives (4b-20)(b+30)=0 Hence b=-30 or 5. Since b cannot be negative we take 5.\r
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\n" ); document.write( "\n" ); document.write( "Checking in [1] gives the area including the borders as (20+2(5))(30+2(5)) = 30 x 40 = 1200 sq ft QED.\r
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\n" ); document.write( "\n" ); document.write( "The width of the border=5ft, \n" ); document.write( "

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