A Norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular window . Find the dimensions of a Norman window of maximum area if the total perimeter is 8ft

Answer 1

So Justin J., (again?)

put the variable "w" in for the width of the rectangle. All the rest of the info is now representable in terms of w. Length, which you might not think is related, IS -- via the total perimeter (you know what the length of the Norman window semicircle is, from circle basics). That gives you relationships among the perimeter dimensions. Then express the total area in terms of the rectangle area plus the semicircular window area, and take the first derivative of that function = 0 to solve for the maximum in the area.

Justin J., If you are having trouble applying your basic algebra and calculus relationships, you might want to consider getting one-on-one tutoring, at least for a while, until you catch up in your course.

--Cheers, --mr. d.