math problem
posted by Anonymous .
A simple rain gutter is constructed using a sheet of aluminum that is 40cm wide. The edges are turned up to form right angles. Determine the depth of the gutter that will maximize the crosssectional area (allowing the greatest amount of water to flow).
I don't know where and how to start.
please help and thank you

make a sketch.
Assuming that the gutter is rectangular and the sides must have the same height, look at the cross section of the gutter.
let the base by y and each of the sides by x
we know that
2x + y = 40
y = 402x
the area A of the crosssection will be
A = xy
= x(402x) = 40x  2x^2
Assuming this is a typical Calculus question ...
dA/dx = 40  4x = 0 for a max of A
404x = 0
x = 10
the the depth will be 10 cm
if you don't know Calculus , you will have to complete the square on
A = 40x  2x^2 
I don't know calculus
This is what I got after completing the square:
A=2(x10)^2+200
How do I know what is the depth when I complete the square?
thank you