document.write( "Question 575194: Find the length and the width of a rectangular garden for a horticultural designer who wants to enclose an area as large as possible with 500 feet of wires \n" ); document.write( "

Algebra.Com's Answer #369428 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
This can be done without calculus.
\n" ); document.write( " I assume this is pre-calculus.
\n" ); document.write( "Let the sides be $\"+x+\"$ , $\"x+\"$ , $\"+y+\"$ , and $\"y\"$
\n" ); document.write( "Let $\"+A+\"$ = area
\n" ); document.write( " $\"+2x+%2B+2y+=+500+\"$
\n" ); document.write( " $\"+2y+=+500+-+2x+\"$
\n" ); document.write( " $\"+y+=+250+-+x+\"$
\n" ); document.write( " $\"+A+=+x%2A%28+250+-+x+%29+\"$
\n" ); document.write( " $\"+A+=+250x+-+x%5E2+\"$
\n" ); document.write( "Because of the minus in front of the $\"+x%5E2+\"$ term,
\n" ); document.write( "this curve has a maximum and not a minimum.
\n" ); document.write( "The maximum occurs at $\"x+=++-%28b%2F%282a%29%29+\"$ when the
\n" ); document.write( "equation has the form $\"+a%2Ax%5E2+%2B+b%2Ax+%2B+c+\"$
\n" ); document.write( " $\"+a+=+-1+\"$
\n" ); document.write( " $\"+b+=+250+\"$
\n" ); document.write( " $\"+-%28b%2F%282a%29%29+=+-%28+250%2F%282%2A%28-1%29%29%29+\"$
\n" ); document.write( " $\"x+=++125+\"$
\n" ); document.write( "and
\n" ); document.write( " $\"+y+=+250+-+x+\"$
\n" ); document.write( " $\"+y+=+250+-+125+\"$
\n" ); document.write( " $\"+y+=+125+\"$
\n" ); document.write( "So the dimensions that maximize the area are A = 125 x 125
\n" ); document.write( "which is a square. ( This is always true when you are maximizing a
\n" ); document.write( "rectangular area ) \n" ); document.write( "

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