Posted by **Anonymous** on Wednesday, April 4, 2012 at 2:09pm.

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 cross-sectional area (allowing the greatest amount of water to flow).

I don't know where and how to start.

please help and thank you

- math problem -
**Reiny**, Wednesday, April 4, 2012 at 2:28pm
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 = 40-2x

the area A of the cross-section will be

A = xy

= x(40-2x) = 40x - 2x^2

Assuming this is a typical Calculus question ...

dA/dx = 40 - 4x = 0 for a max of A

40-4x = 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

- math problem -
**Anonymous**, Wednesday, April 4, 2012 at 2:43pm
I don't know calculus

This is what I got after completing the square:

A=-2(x-10)^2+200

How do I know what is the depth when I complete the square?

thank you

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