document.write( "Question 105520This question is from textbook Larson Hostetler Algebra and Trigonomnetry
\n" ); document.write( ": A rectangular playing field with a perimeter of 100 meters is to have and area of at least 500 square meters. Within what bounds must the length of the rectangle lie? \n" ); document.write( "

Algebra.Com's Answer #77231 by alvinjohnburgos(11) $\"\"$ $\"About$

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If we represent length and width as L and W, respectively:
\n" ); document.write( "The rectangular field must have an area of at least 500sqm (to make it easier, we will use equal sign instead of the greater-than-or-equal sign:
\n" ); document.write( "eq1 $\"LW+=+500\"$
\n" ); document.write( "Perimeter is 100m:
\n" ); document.write( "eq2 $\"2L+%2B+2W+=+100\"$
\n" ); document.write( "First, isolate W in eq2:
\n" ); document.write( " $\"2W+=+100+-+2L\"$
\n" ); document.write( " $\"W+=+50+-+L\"$
\n" ); document.write( "Then, substitute (50 - L) for W in eq1:
\n" ); document.write( " $\"L%2850-L%29+=+500\"$
\n" ); document.write( " $\"50L+-+L%5E2+=+500\"$
\n" ); document.write( " $\"L%5E2+-+50L+%2B+500+=+0\"$
\n" ); document.write( " $\"L%5E2+-+50L+=+-500\"$
\n" ); document.write( " $\"L%5E2+-+50L+%2B+625+=+125\"$
\n" ); document.write( " $\"%28L+-+25%29%5E2+=+125\"$
\n" ); document.write( " $\"L+-+25+=+%2B-5sqrt%285%29\"$
\n" ); document.write( " $\"L+=+25+%2B-5sqrt%285%29\"$
\n" ); document.write( "Since L > W:
\n" ); document.write( " $\"L+=+25+%2B+5sqrt%285%29\"$
\n" ); document.write( "Since lessening the value of L until 25 makes the area greater:
\n" ); document.write( " $\"25m+%3C=+L+%3C=+%2825+%2B+5sqrt%285%29%29m\"$ \n" ); document.write( "

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