document.write( "Question 690215: roger has 144 feet of fencing material to enclose a rectangular exercise yard for his dog. one side of the yard will border his house, so he will only need to fence three sides. find the maximum area of the yard? \n" ); document.write( "

Algebra.Com's Answer #426212 by josmiceli(19441) $\"\"$ $\"About$

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There is a side parallel to the house and there
\n" ); document.write( "are 2 equal sides perpendicular to the house
\n" ); document.write( "Call each of the sides perpendicular
\n" ); document.write( "to the house $\"+s+\"$
\n" ); document.write( "The side parallel to the house is
\n" ); document.write( " $\"+144+-+2s+\"$ ft long
\n" ); document.write( "The area, $\"+A+\"$ is
\n" ); document.write( "(1) $\"+A+=+s%2A%28+144+-+2s+%29+\"$
\n" ); document.write( "(2) $\"+A+=+-2s%5E2+%2B+144s+\"$
\n" ); document.write( "This is a parabola with a maximum, because of
\n" ); document.write( "the minus sign in front of the $\"+x%5E2+\"$ term
\n" ); document.write( "The maximum is midway between the 2 roots
\n" ); document.write( "To find the roots:
\n" ); document.write( "(1) $\"+0+=+s%2A%28+144+-+2s+%29+\"$
\n" ); document.write( " $\"+s+=+0+\"$
\n" ); document.write( " $\"+144+-+2s+=+0+\"$
\n" ); document.write( " $\"+2s+=+144+\"$
\n" ); document.write( " $\"+s+=+72+\"$
\n" ); document.write( " $\"+%28+72+%2B+0+%29+%2F+2+=+36+\"$
\n" ); document.write( "The maximum is at (s,A) = (36,A)
\n" ); document.write( "Now find $\"+A+\"$
\n" ); document.write( " $\"+A+=+-2%2A36%5E2+%2B+144%2A36+\"$
\n" ); document.write( " $\"+A+=+-2592+%2B+5184+\"$
\n" ); document.write( " $\"+A+=+2592+\"$
\n" ); document.write( "The maximum area is 2592 ft2
\n" ); document.write( "check answer:
\n" ); document.write( "Here's the plot:
\n" ); document.write( " $\"+graph%28+400%2C+400%2C+-20%2C+80%2C+-200%2C+2800%2C+-2x%5E2+%2B+144x+%29+\"$
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