Hi

I need help on the following question:

1) A symmetrical gutter is made of metal sheeting 30cm. wide by bending it twice as shown in the cross section. Find an expression for the area $\displaystyle A(\theta)$ of the cross section and hence find the value of $\displaystyle \theta$ for the gutter to have maximum carrying capacity.

This is what i have try to do so far.

I know that Area of a square is L*W and Area of 2 triangles is $\displaystyle 2(0.5*x^2 * sin(\theta))$

so $\displaystyle L*W + x^2 * sin(\theta) = 30$

Make $\displaystyle W = \frac{30 - x^2(sin(\theta))}{10}$

$\displaystyle A = L*W$

$\displaystyle A = 10(\frac{30 - x^2(sin(\theta))}{10})$

$\displaystyle A = 30 - x^2(sin(\theta))$

$\displaystyle A' = -x^2(\frac{dA}{d\theta})cos(\theta) + 2xsin(\theta)$

$\displaystyle A' = \frac{2xsin(\theta)}{-x^2(cos(\theta))}$

Don't think this is correct.

P.S