document.write( "Question 1021424: Aleah's garden borders a wall. She buys 80 meters of fencing. What dimensions maximize the area of the garden. \n" ); document.write( "

Algebra.Com's Answer #637204 by Fombitz(32388) $\"\"$ $\"About$

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There are three borders using the fencing.
\n" ); document.write( " $\"2L%2BW=80\"$
\n" ); document.write( "The area is then,
\n" ); document.write( " $\"A=L%2AW\"$
\n" ); document.write( "Substituting from the perimeter,
\n" ); document.write( " $\"A=L%2880-2L%29\"$
\n" ); document.write( "It's a quadratic, convert to vertex form.
\n" ); document.write( " $\"A%28L%29=80L-2L%5E2\"$
\n" ); document.write( " $\"A%28L%29=-2L%5E2%2B80L\"$
\n" ); document.write( " $\"A%28L%29=-2%28L%5E2-40L%29\"$
\n" ); document.write( " $\"A%28L%29=-2%28L%5E2-40L%2B400%29%2B2%2A400\"$
\n" ); document.write( " $\"A%28L%29=-2%28L-20%29%5E2%2B800\"$
\n" ); document.write( "So the maximum occurs when $\"L=20\"$ $\"m\"$ and the value is $\"A%2820%29=800\"$ $\"m%5E2\"$
\n" ); document.write( "Then,
\n" ); document.write( " $\"20%2AW=800\"$
\n" ); document.write( " $\"W=40\"$ $\"m\"$
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