Max/min problem, find max area of sector of circle. 
A sector of a circle has fixed perimeter. For what central angle $θ$ (in radians) will the area be greatest?


First I put together an equation for the perimiter of the sector being $p$ which I assume as a constant since it is fixed:
$$p = rθ + 2r$$
Since p is a contant and need to reduce the number of variables to one in the area equation before diffrenciating, I rearranged the equation in terms of $r$:
$$r = \dfrac{p}{θ + 2}$$
I noticed, since the perimeter is constant, $θ$ and $r$ must be inverse proportional to another, problem is I wasn't sure what the coefficient proportionality or constant ($p$) was, so I assumed it to be $1$:
$$r = \dfrac{1}{θ + 2}$$
I then plugged that back into the area of a sector forumla and diffrenciated with respect to $θ$:
$$\dfrac{d}{dθ}{(\dfrac{θ}{2(θ+2)^2})}=\dfrac{2(θ+2)^2-θ(4(θ+2))}{(2(θ+2)^2)^2}$$
I put that equal to zero and solved for theta and received 2 radians.
Did I do this correctly? if so, was I to assume the $p$ to be 1? or is there a way of calculating it? constructive criticism is welcome.
Thanks

The area $A$ of a sector is $A = (1/2)(R^2)(\theta)$.
Substitute $R = {P \over {(\theta + 2)}}$ where $P$ is perimeter in above equation then differentiate w.r.t $\theta$. Then equate it to zero to find theta for which Area is Max.
Leave $P$ as it is. Don't put it equal to 1. Treat it as you treat constants.
Note: I am sorry I could not use latex as I am on mobile device. 
