Find the dimensions of a Norman window of maximum area if the total perimeter is 28 feet.

Question

A Norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular window (see figure). Find the dimensions of a Norman window of maximum area if the total perimeter is 28 feet.

Answer 1

The solution to this problem is messy, but not difficult.

The perimeter is πr + 2h + 2r = 28

Solve this for h in terms of r: h=(1/2)[28-(π+2)r]

Then A = (1/2)πr² + (1/2)r[28-(π+2)r]

Differentiate A with respect to r and set that derivative = 0.

Solve for r and then go back to get h.