document.write( "Question 36521: Amanda has 400 feet of lumber to frame a rectangular patio (the perimeter of a rectangle is 2 times length plus 2 times width). She wants to maximize the area of her patio (area of a rectangle is length times width). What should the dimensions of the patio be, and show how the maximum area of the patio is calculated from the algebraic equation. \n" ); document.write( "

Algebra.Com's Answer #22431 by Paul(988) $\"\"$ $\"About$

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So thats:
\n" ); document.write( "2l+2w=400
\n" ); document.write( "l=200-w (subsituttion)
\n" ); document.write( "Area:
\n" ); document.write( "lw=A
\n" ); document.write( "Subsitute:
\n" ); document.write( "(200-w)(w)=A
\n" ); document.write( "200w-w^2=A
\n" ); document.write( "Differentate:
\n" ); document.write( "2w=200
\n" ); document.write( "w=100
\n" ); document.write( "Hence, the width and length are 100 ft each and the area is 100^2 ft squared.
\n" ); document.write( "Paul. \n" ); document.write( "

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