document.write( "Question 399521: A farmer has a rectangular garden plot surrounded by 120ft of fence. Find the length and width of the garden if its area is 800 square feet. \n" ); document.write( "

Algebra.Com's Answer #282894 by josmiceli(19441) $\"\"$ $\"About$

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Let the width = $\"w\"$ ft
\n" ); document.write( "The length will be $\"800%2Fw\"$ ft
\n" ); document.write( "Also,
\n" ); document.write( " $\"2w+%2B+2%2A%28800%2Fw%29+=+120\"$ ft
\n" ); document.write( "Multiply both sides by $\"w\"$
\n" ); document.write( " $\"2w%5E2+%2B+1600+=+120w\"$
\n" ); document.write( " $\"2w%5E2+-+120w+%2B+1600+=+0\"$
\n" ); document.write( " $\"w%5E2+-+60w+%2B+800+=+0\"$
\n" ); document.write( "I can solve by completing the square:
\n" ); document.write( " $\"w%5E2+-+60w+%2B+%2860%2F2%29%5E2+=+-800+%2B+%2860%2F2%29%5E2\"$
\n" ); document.write( " $\"w%5E2+-+60w+%2B+900+=+-800+%2B+900\"$
\n" ); document.write( "Both sides are perfect squares
\n" ); document.write( " $\"%28w+-+30%29%5E2+=+10%5E2\"$
\n" ); document.write( "Take the square root of both sides
\n" ); document.write( " $\"w+-+30+=+10\"$
\n" ); document.write( " $\"w+=+40\"$
\n" ); document.write( "There is a negative root also:
\n" ); document.write( " $\"w+-+30+=+-10\"$
\n" ); document.write( " $\"w+=+20\"$
\n" ); document.write( "The length is 40 and the width is 20
\n" ); document.write( "check:
\n" ); document.write( " $\"2%2A40+%2B+2%2A20+=+80+%2B+40\"$
\n" ); document.write( " $\"80+%2B+40+=+120\"$ OK
\n" ); document.write( " $\"area+=+40%2A20+=+800\"$ ft2
\n" ); document.write( "OK \n" ); document.write( "

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