document.write( "Question 33414: The perimeter of a rectangle window is 32 ft. Find the dimension of the window that will enclose the largest area. \n" ); document.write( "

Algebra.Com's Answer #19773 by Paul(988) $\"\"$ $\"About$

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Perimeter is 2w+2L=32
\n" ); document.write( "sOLVE FOR L
\n" ); document.write( "l=16-w (subsistuion)
\n" ); document.write( "Max Area is A:
\n" ); document.write( "(w)(l)=A
\n" ); document.write( "Subsitute for l:
\n" ); document.write( "(w)(16-w)=A
\n" ); document.write( "-w^2+16w=A
\n" ); document.write( "Differentate with respect to w:
\n" ); document.write( " $\"dA%2Fdt=%28-2w%29dw%2Fdt%2B%2816%29dw%2Fdt\"$
\n" ); document.write( "-2w=-16
\n" ); document.write( "w=8
\n" ); document.write( "l=16-8
\n" ); document.write( "l=8
\n" ); document.write( "8^2=64
\n" ); document.write( "Hence, the largest area you can have is 64ft^2 with length of 8ft and width of 8ft.
\n" ); document.write( "Paul. \n" ); document.write( "

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