A drain is to be made up of rectangular aluminum sheets 12 inches wide by turning up the side edges 90 degrees. What depth (of the edges) will provide a maximum cross sectional area and thereby provide for the greatest flow of water
A drain is to be made up of rectangular aluminum sheets 12 inches wide by turning up the side edges 90 degrees. What depth (of the edges) will provide a maximum cross sectional area and thereby provide for the greatest flow of water
Let the length of the fold be x inches. Then the base will have length 12-2x inches. By using $\displaystyle x=\frac{-b}{2a}$ we can find the length of the folded side to maximize area.
Area = $\displaystyle x(12-2x)=-2x^{2}+12x$
a=-2 and b=12
$\displaystyle x=-\frac{12}{2(-2)}=3$
Turn the edges up 3 inches.