A Norman window has the shape of a rectangle with a semi circle on top; diameter of the semicircle exactly matches the width of the rectangle. Find the dimensions of the Norman window whose perimeter is 300 in that has maximal area.
The area of the semicircle would be $(\pi(w/2)^2)/2$. The area of the rectangle would be $hw$. I know that the perimeter is 300 in, and that the perimeter would be $2h+w+(w\pi) = 300$. How would I write $h$ in terms of $w$, and then solve for $h$ to specify the dimensions? The total area would be the 2 sub-areas added together. I would have to take the derivative of the combined areas to solve for the width and height. What would be the proper steps for doing this?